Oil light stays on too long on a cold start

I seemed to have had similar in my 2.4L Plymouth engine. I didn't like the tiny factory oil filter, so went to a larger diameter one that my 3.8L uses (based on web recommendations). While it fit fine, seems I heard more noise initially from the overhead valve-train after start-up, like the oil had drained back. Seems that decreased when I went back to the normal small oil filter. I think that silicone flap you see thru the holes in the bottom of an oil filter serves as the anti-drainback. But, in my case, the oil lamp went off right away with either filter.