How do I know my tax payment was received through TurboTax? I answered all the payment questions such as routing and account number.

It is transmitted with your return to the IRS.  TurboTax does not take the payment out.  The IRS does.  So you will need to watch your bank for when they take the payment out. TurboTax has no knowledge, update or information on the payment after it is transmitted to the IRS.