It appears that if you don’t receive the email within 2-3 days of dining, it won’t be triggered.
Unfortunately, with hundreds if not thousands of participating restaurants, this seems to be very hit or miss, depending on how the restaurant POS systems are set up. I feel like this has not been implemented well by Amex and is just going to cause frustration for people.
I recently dined at a Resy restaurant located inside a hotel, and when the charge was processed, it was under the hotel’s account. Not surprisingly, it did not trigger the credit.