Your proof of payment is the cancelled check if you paid the taxes owed by check. Or it will be your bank or credit card statement showing the payment if you used direct debit from your bank or paid the taxes owed by credit card.
TurboTax does not pay the taxes owed.
If you selected to pay by direct debit from your bank account, that information is sent with your tax return and the IRS debits your account.
How you chose to pay the taxes owed will be on the Filing Instructions page of your tax return. It will also be on the Federal Information Worksheet Part V.
Your only proof of payment is your bank statement or credit card showing the payment coming out. Turbo Tax only passes your bank account number to the IRS or state for them to take it out of your account. (Most states do not let you pay by Direct Debit so you have to mail in a check or go directly to the state's website to pay). And some banks use different routing numbers for deposits and payments. Double check the number you entered with your bank.