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When the hotels prepare the rooms they know the status of each guest based on other data in the reservation. So Golds/Diamonds staying at a Hampton get the water & cookies, etc.
When I make a stay with a higher status than I had when I booked the stay I usually show my card at checkin. It generally won't make a lot of difference if you check in as a Diamond and the reservation record shows you as Gold since the systemwide perks don't differ much. There may be local exceptions where the property extends a courtesy to a Diamond that they wouldn't to a Gold. I've seen parking fees waived in the US or lounge access granted overseas for Diamonds only. In most/all cases showing your new status card at checkin should get you what you deserve.