DME runs 24 hrs. They stop automatic luggage delivery for arrivals after 10pm. Just to be safe, you should pack what you might need for the 1st 24 hours in your carry-on, that way if things are delayed, you won't be stuck waiting for your bags. This is good advice for anytime you fly, not just when it applies to DME. Bags are rarely lost forever, but are misdirected by the airlines many times. If you have PJs, bathing suits, toiletries, and clothes for the next day, you'll be good to go
You should likely see your bags delivered that night, but if it's starting to get late, and you want to go to bed, you can call Luggage Assistance, ask them to hold your DME bags until morning, and put out the Do Not Disturb tag. Then in the morning, you can call, and ask to have your DME bags delivered.