The problem is not the dome light position set to ON, because it's off when the car is off. I had this problem once, I don't know if it's the same for you... It may be a short circuit with some ground around the car. The way the lights work is by switching the negative (instead of the positive like most switched electrical circuits). So if a negative wire coming from the doors or going to the foot lights is touching a ground that comes on while the car is on, it will be on always when the car is on and off while the car is off. If you want to fix it, you may need to check all the wire all the way.
It happened to me when I modded my interior lights. I plugged neons to my foot lights so they could lit up when I oppened my door, but I wanted them so be switched also, but I didn't know it was the negative that was wired for the interior lights, so the same problem as you occured. I just fixed my circuit to make it work correctly.