Aux. Power Relay

I have a issue I would like some help with. I have remote start and if I decide that I don't want to leave after it's already started, I shut it off and the stereo and electronics in the interior are still on. They stay on until a door is opened.

This sounds like the work of a relay that causes everything to stay on. If it is a relay, which on is it? I want to get around it. If it's not then what cause this and is there any fixes?