Not really. If the extracted camera is right with the c4d file, then any 3d elements you insert in the scene should just stay put. Are you sure you extracted the right camera?
There was only one camera set up in c4d. I extracted that info which set up one camera in the AE comp. I then took 2D clouds, made them 3D and placed them in the scene. the camera does a left to right move and as it does, the C4D file moves with a delay of several frames on the newly inserted clouds.
That's very odd. Try the same thing with just a cube. The tricky part is lineing up your 3D layers so they match the position of your scene. If your planes don't line up then the parallax won't work and the perspective shift will be odd. It's hard to see without a top view of your comp but I think your cloud layer isn't in the right place in the comp.
You could try working in reverse. Set you cloud layer and a camera in AE and create a c4d file from the comp.
Did you make sure that you're using the Comp camera in cineware and that the camera was extracted at frame 0?
I can't work in reverse becasue the camera move is complicated and the camera preview in C4D is a LOT faster then AE.
I will double check to be sure that I have the comp cam selected and that I extracted at frame 0.