1 night stay on 3/4 - Received bill on 3/5, received hyatt points
1 night stay on 3/5 - did not receive bill, no hyatt points yet
2 night stay on 3/6 - did not receive bill, no hyatt points yet

I called Rio billing and they sent me the bills instantly. They had to manually remove the Hash House charges ($55, $55, and $105) but it may be unique to me. The breakfasts were charged to that day's reservation rather than the preceding day.

Honestly customer service has been amazing so far.