That's really strange I've never heard of that before. The front switch by the main dome light (above the shifter) has three positions. Always off / On when doors open / Always on. Do they even stay on with the switch in the "always off" position?
What's weird is that on 325s all interior lights should come on at once with any door open, not just the rear. Maybe the bulb was pulled from the main dome light up front. That would mean the car thinks a door's closed, so check all the latches/sensors on the doors.
1998 BMW 328is - summer
1994 BMW 325i - daily
1992 BMW 325i - totaled
1988 Mercedes Benz 190E 2.3-8V - sold