Do I need to send my payments for taxes due after paying Turbo to file them for me?

You pay the TurboTax account fees in the File section of the program in Step 1.  After completing Step 1 the program will take you to Step 2.  In Step 2, when taxes are owed, you are give several options on how to pay the taxes owed.

Some clarification is needed here.

 TurboTax does not file any tax return for anyone under any circumstances. There are no exceptions. What you pay TurboTax for, is the use of their software to prepare and e-file your tax return, and that's it.

Only you can file your return. If you elect to e-file then only you can click that big orange TRANSMIT MY RETURNS NOW button to e-file it. If you elect to mail the return to the IRS, then only you can elect the "Print and File" option. After it's printed it's up to you to sign and mail the return to the IRS, as well as to your state if applicable.

When you owe taxes, be it to the IRS, your state, or any other taxing authority, Turbotax does not, will not, and can not act as a middleman in that transaction. To pay any taxes due to the IRS you can do so online at www.irs.gov/payments.  If you owe your state then you'll have to check your state's website for payment options. Not all states offer the ability to pay taxes due online.