it stays on because your remote wire is connected to a 12 v constant wire. you need it to be connected to a switched wire that is only on when your car is on.
Why do shops do this sometimes? I had a freind who had a system in his mustang and while doing something in his trunk with the car off I noticed that his amps were still on and asked him about it and he said idk they've always been like that. Is it just out of laziness?
Just as a heads up it could be a problem with the amp as well, remove the remote wire and make sure it turns the amp off. I had an opti2000 that would stay on without a remote wire hooked up.