Correct. He’ll get the refund the day after a clerk reviews the transactions and clicks the refund button. The “Please allow N–M weeks…” verbiage you find in many types of contracts is just the other party giving themselves time to conduct that manual review. It should never be taken as an estimate of how long the other party thinks it will actually take.
More likely process for refund will start when system or someone reviews the refund and approves it. That might also take some time to be processed. I can imagine that their systems generally don't need to be exactly fast and might have very old integrations.
