If you entered your bank account and routing number the IRS should pull it out of your account. Turbo Tax doesn't pay or send your tax due. It only transmits your bank info to the IRS. Then the IRS debits your account on the date you specified or later. It may take them longer to pull it. I don't think they ever debit your account right away as soon as you file. You need to give them time to process your return and payment.
Your only proof of payment is your bank statement or credit card showing the payment coming out. And the IRS or state does not update Turbo Tax when or if they get your payment.