The postmark isn't the stamp (piece of paper). It's the ink seal that's stamped over the stamp with the date on it. It doesn't matter how you pay for the piece of mail; it now potentially get postmarked at a later date than previously.
Request a Manual Postmark: Customers may present a mail piece at a retail counter and request a "manual (local) postmark". This postmark is applied at the time of acceptance, so the date aligns with the date the USPS took possession.
I should have said manual postmark but it’s what I implied. They’re stamping or postmarking it with a date manually.