As part of the dues for each calendar year,
DVC estimates the amount that will be needed for the property taxes. As owners we give them that money in January if we pay in full or monthly throughout the year for those who make monthly payments. Disney gets the tax bill in November I believe and pays it at that time. In December when we get our dues bill for the following year. The bill lists the actual property tax paid for the current year and whether we owe additional money (if the estimated taxes were less than the actual billed amount). Any additional amount due is added to the dues for the next calendar year.
The OP purchased the contract part way through 2015 so he/she did own the property during part of the 2015 tax year and reimbursed the seller for the 2015 dues which included the estimated tax payments for 2015. The OP's 2016 dues bill will show the actual property taxes paid for 2015 so that information could be provided to the IRS in the very unlikely event this deduction is ever questioned due to the tax information not being broken out in the closing statement.