Depending on how you choose to pay the taxes owed, your proof of payment will either be a cancelled check or bank or credit card statement showing the amount paid.
You need your own canceled check, bank or credit card records to prove to the IRS that you paid. Do you have that? TurboTax never knows how, when or even if you paid your tax due, and cannot provide any proof to the IRS that you paid. When you look at the filing instructions that print out with your tax return, what does it show for how you were paying your tax due?
You do not pay your tax to TurboTax, and TurboTax does not pay your tax to the IRS. If you chose to pay your federal tax by direct debit, TurboTax just sends your bank account information to the IRS along with your tax return. If you did not pay by direct debit, you have to either mail a check to the IRS, pay online on the IRS web site, or pay by credit card through a third-party payment processor.
Your proof that your tax was paid is your bank account records or credit card statement showing the payment to the IRS.