Given correct responses to TurboTax's questions, TurboTax's calculation of the maximum contribution will be correct.
If your HDHP plan was self-only and you are over age 55, your maximum HSA contribution would be
$4,550 * 9 / 12 = $3,412.50. This is the result that you will see (rounded to $3,413) if you tell TurboTax that you had self-only coverage for January through September and Medicare for October through December.
