Teach him, and tell him outright. My nephew would leave the water run for 5-10 minutes BEFORE he would take a shower. I was like, "Dude, you may do that in your house, but not here. We ALL need the hot water, and we all need to use the bathroom. Speed it up." And he got the idea that at Aunt GN's house, it's different.
I've found that with a lot of kids and young adults, if you let them know that you're holding them accountable, they'll step up to the plate. His parents and grandparents probably never did. If he knows he can't get away with sloppiness with you, then he may just 'behave'.
Start out when you show him the bathroom by saying something like, "Here's a towel and washcloth. Soap is there. This shower doesn't have a door, so you have to make sure the curtain stays on the inside when you shower. You know, Aunts remember all of those embarrassing things, like when you flooded the bathroom at grandma and grandpa's. So DON'T let any of the water get out of the tub, or when it leaks into the apartment downstairs, because it WILL, YOU are going to be the one to explain to the downstairs neighbors why you can't shower without creating a monsoon. Got it?" Say it in a good-natured, semi-joking way, but at the same time, let him know that you're serious. Make him know he's accountable.
Better yet, get one of those squeegees for the shower. Even if you don't normally use one, pretend you do. Then show him how to squeegee the walls, "so it doesn't get musty smelling" while it dries. See, it's another thing to make him conscious of doing. And the more things he's conscious of, the more likely he'll be to take some care.
(And make sure he knows that the curtain has to be firmly around the edge where the faucet is. That's where all of my shower-curtain leakage seems to occur, b/c of the spray splashing off your body.)