For TurboTax purposes, you have it correct - you should report your Form 1098 amounts for property tax paid in the mortgage interest section. And, then report the rest under the general property tax amounts section, which is right below the mortgage interest section on the Deductions and Credits page.
But, this is really just a "best practice" way of reporting and recordkeeping. In the end, property taxes get totaled on Line 6 of Schedule A and the Schedule does not make a distinction between property taxes paid by your mortgage company or yourself (unlike mortgage interest).
