It's been a while since I last used it in a physical place, but basically the store's or restaurant's payment system accepted the payment as soon as the transaction was broadcast over the network. In other words, payment was instantaneous. The system did not wait for a confirmation block. That's not unreasonable, since every transaction with nonzero fees was eventually confirmed, in those early days before the network got clogged up.

Not sure how it would work now, but I think even now chances are that the transaction would eventually be confirmed, so the POS system could gamble on that and "accept" it if it includes some minimal fee.