Am I required to file an extension form if the payment requirements to receive an extension have been met?

No. The extension is automatic if the payment requirements for receiving an extension have been met.  TNTAP has a drop down box to indicate when a payment is for an extension; otherwise, there is not a place or a need to formally request an extension.  Paper Form FAE 173 is for taxpayers that meet an exception for filing electronically and that are submitting a payment.