If you're lucky -- within 3-5 days. I've found it's less about time delta from checkout and more likely X property processes their Hyatt partner stay credit on Y day (like Sat or Sun).

If you're not lucky, it never shows up, and you have to wait a full 30 days before you can even raise a request with the MGM side to look up and re-process the credit.

You can always pull your concierge into it if you have one -- but I don't have any data points on that having expedited the process. Would love to know if it does.