Moving in and out points of layers into a new comp

I'm in a bind. I'm creating a complex moving split screen scene. First I chose in and out points for all my video clips (about thirty of them) in Premiere Pro, and made a rough plan of what it should look like. Then I Dynamic-Linked it to After Effects.

I left that comp alone and then created a new comp to create moving layer solids for the split screen animation. (Colored rectangles flying around.) So far so good. The plan was then to drag and drop the video clips onto the layer solids (which all have masks) but when I drag it over, it ignores the in and out point.

Is there a way to get it to recognize the in and out point? The in and out points are just fine in the Dynamic Link comp. (Again, that comp is just a very rough cut with no resizing or animation. I just did it to get the timing down.) Thanks.