<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><Version>2.4.0.8</Version><ReportLongName>057 - Disclosure - MORTGAGE SERVICING RIGHTS- Mortgage Servicing Rights Measured using Amortization Method with Aggregate Activity in Related Valuation Allowances - Activity in the balance of mortgage servicing rights, measured using the amortization method (Details)</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode>USD</CurrencyCode><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol>$</CurrencySymbol><contextRef><ContextID>Context_6ME__30-Jun-2013</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0001484949</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2013-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2013-06-30T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS><UnitProperty><UnitID>USD</UnitID><UnitType>Standard</UnitType><StandardMeasure><MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema><MeasureValue>USD</MeasureValue><MeasureNamespace>iso4217</MeasureNamespace><MeasureDescription /><MeasureType /></StandardMeasure><Scale>0</Scale></UnitProperty></UPS><CurrencyCode>USD</CurrencyCode><OriginalCurrencyCode>USD</OriginalCurrencyCode></MCU><CurrencySymbol>$</CurrencySymbol><Labels><Label Key="CalendarSupplement" Id="0" Label="6 Months Ended" /><Label Key="Calendar" Id="1" Label="Jun. 30, 2013" /></Labels></Column><Column FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode>USD</CurrencyCode><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol>$</CurrencySymbol><contextRef><ContextID>Context_FYE__31-Dec-2012</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0001484949</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2012-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2012-12-31T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS><UnitProperty><UnitID>USD</UnitID><UnitType>Standard</UnitType><StandardMeasure><MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema><MeasureValue>USD</MeasureValue><MeasureNamespace>iso4217</MeasureNamespace><MeasureDescription /><MeasureType /></StandardMeasure><Scale>0</Scale></UnitProperty></UPS><CurrencyCode>USD</CurrencyCode><OriginalCurrencyCode>USD</OriginalCurrencyCode></MCU><CurrencySymbol>$</CurrencySymbol><Labels><Label Key="CalendarSupplement" Id="0" Label="12 Months Ended" /><Label Key="Calendar" Id="1" Label="Dec. 31, 2012" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>1</Level><ElementName>us-gaap_TransfersAndServicingAbstract</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell><Cell FlagID="0" ContextID="" UnitID=""><Id>2</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Transfers And Servicing [Abstract]</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>jxsb_MortgageServicingRightsAcquisition</ElementName><ElementPrefix>jxsb_</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>debit</BalanceType><PeriodType>instant</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>true</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>periodStartLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="Context_As_Of__31-Dec-2012" UnitID="USD"><Id>1</Id><IsNumeric>true</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>664436</NumericAmount><RoundedNumericAmount>664436</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode>USD</CurrencyCode><CurrencySymbol>$</CurrencySymbol><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>true</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell><Cell FlagID="0" ContextID="Context_As_Of__31-Dec-2011" UnitID="USD"><Id>2</Id><IsNumeric>true</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>697733</NumericAmount><RoundedNumericAmount>697733</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode>USD</CurrencyCode><CurrencySymbol>$</CurrencySymbol><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>true</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:monetaryItemType</ElementDataType><SimpleDataType>monetary</SimpleDataType><ElementDefenition>Mortgage Servicing Rights Acquisition</ElementDefenition><ElementReferences>No definition available.</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>2</UnitID><Label>Balance, beginning of year</Label></Row><Row FlagID="0"><Id>3</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>jxsb_MortgageServicingRightsCapitalized</ElementName><ElementPrefix>jxsb_</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>debit</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>terseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="Context_6ME__30-Jun-2013" UnitID="USD"><Id>1</Id><IsNumeric>true</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>63515</NumericAmount><RoundedNumericAmount>63515</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell><Cell FlagID="0" ContextID="Context_FYE__31-Dec-2012" UnitID="USD"><Id>2</Id><IsNumeric>true</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>219975</NumericAmount><RoundedNumericAmount>219975</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:monetaryItemType</ElementDataType><SimpleDataType>monetary</SimpleDataType><ElementDefenition>Mortgage Servicing Rights Capitalized</ElementDefenition><ElementReferences>No definition available.</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>2</UnitID><Label>Servicing rights capitalized</Label></Row><Row FlagID="0"><Id>4</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>us-gaap_AmortizationOfMortgageServicingRightsMSRs</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>debit</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>true</IsReverseSign><PreferredLabelRole>negatedLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="Context_6ME__30-Jun-2013" UnitID="USD"><Id>1</Id><IsNumeric>true</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>-85946</NumericAmount><RoundedNumericAmount>-85946</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell><Cell FlagID="0" ContextID="Context_FYE__31-Dec-2012" UnitID="USD"><Id>2</Id><IsNumeric>true</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>-297784</NumericAmount><RoundedNumericAmount>-297784</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:monetaryItemType</ElementDataType><SimpleDataType>monetary</SimpleDataType><ElementDefenition>The periodic amortization (in proportion to and over the period of estimated net servicing income or loss) of capitalized servicing rights, which contractually entitle the servicer to receive fees and ancillary revenues for performing billing, collection, disbursement and recordkeeping services in connection with a mortgage portfolio. As a noncash expense, this element is added back to net income when calculating cash provided by or used in operations using the indirect method.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 230

 -SubTopic 10

 -Section 45

 -Paragraph 28

 -Subparagraph (b)

 -URI http://asc.fasb.org/extlink&amp;oid=31042434&amp;loc=d3e3602-108585



Reference 2: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 860

 -SubTopic 50

 -Section 50

 -Paragraph 4

 -Subparagraph (a)(4)

 -URI http://asc.fasb.org/extlink&amp;oid=7882072&amp;loc=d3e122739-111746



</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>2</UnitID><Label>Amortization of servicing rights</Label></Row><Row FlagID="0"><Id>5</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>jxsb_MortgageServicingRightsAmortizationAndValuationAllowanceAdjustmentsNet</ElementName><ElementPrefix>jxsb_</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>debit</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>terseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="Context_6ME__30-Jun-2013" UnitID="USD"><Id>1</Id><IsNumeric>true</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>12472</NumericAmount><RoundedNumericAmount>12472</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell><Cell FlagID="0" ContextID="Context_FYE__31-Dec-2012" UnitID="USD"><Id>2</Id><IsNumeric>true</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>44512</NumericAmount><RoundedNumericAmount>44512</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:monetaryItemType</ElementDataType><SimpleDataType>monetary</SimpleDataType><ElementDefenition>Mortgage Servicing Rights Amortization And Valuation Allowance Adjustments, Net</ElementDefenition><ElementReferences>No definition available.</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>2</UnitID><Label>Change in valuation allowance</Label></Row><Row FlagID="0"><Id>6</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>jxsb_MortgageServicingRights</ElementName><ElementPrefix>jxsb_</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>debit</BalanceType><PeriodType>instant</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>true</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>periodEndLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="Context_As_Of__30-Jun-2013" UnitID="USD"><Id>1</Id><IsNumeric>true</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>654477</NumericAmount><RoundedNumericAmount>654477</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode>USD</CurrencyCode><CurrencySymbol>$</CurrencySymbol><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>true</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell><Cell FlagID="0" ContextID="Context_As_Of__31-Dec-2012" UnitID="USD"><Id>2</Id><IsNumeric>true</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>664436</NumericAmount><RoundedNumericAmount>664436</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode>USD</CurrencyCode><CurrencySymbol>$</CurrencySymbol><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>true</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:monetaryItemType</ElementDataType><SimpleDataType>monetary</SimpleDataType><ElementDefenition>Represents net future revenues from contractually specified servicing fees, late charges, and other ancillary revenues, in excess of future costs related to servicing arrangements for mortgage loans. Mortgage servicing rights may be obtained via (1) acquisition or assumption of a servicing obligation that does not relate to financial assets of the service or its consolidated affiliates; or (2) by originating loans and then (a) transferring the loans to a qualifying special purpose entity in a transaction that meets the necessary transfer and classification requirements, or (b) transferring the loans in a transaction that meets the requirements for sale accounting.</ElementDefenition><ElementReferences>No definition available.</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>2</UnitID><Label>Balance, end of period</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>MORTGAGE SERVICING RIGHTS- Mortgage Servicing Rights Measured using Amortization Method with Aggregate Activity in Related Valuation Allowances - Activity in the balance of mortgage servicing rights, measured using the amortization method (Details) (USD $)</ReportName><MonetaryRoundingLevel>NoRounding</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>true</HasCustomUnits><IsEmbedReport>false</IsEmbedReport><IsMultiCurrency>false</IsMultiCurrency><ReportType>Sheet</ReportType><RoleURI>http://www.jacksonvillesavings.com/role/MORTGAGESERVICINGRIGHTSMortgageServicingRightsMeasuredUsingAmortizationMethodWithAggregateActivityInRelatedValuationAllowancesActivityInTheBalanceOfMortgageServicingRightsMeasuredUsingTheAmortizationMethodDetails</RoleURI><NumberOfCols>2</NumberOfCols><NumberOfRows>6</NumberOfRows></InstanceReport>
