Problem with scaling

Your workflow is flawed from the start. If you need to Warp Stabilize (completely different than stabilize) the footage and then do other things to the footage the only sensible option for a shot that is more than a couple of seconds long is to run warp stabilize on the footage separately, render a digital intermediate to a lossless format and then do the rest of your processing on the repaired footage. If the shot is only a couple of seconds long you can get away with putting the footage in a separate composition, running warp stabilizer on the footage, and then using that comp as a layer in your main comp. Any footage that you have applied warp stabilizer to should be in it's own comp with no other effects applied or other layers in the comp.

good point on rendering the segment in premiere, this may be required since some of the effects won't pass through smoothly. bare in mind that render and replace (clip->render and replace) won't work for nested sequences, just for clips. if you want the whole sequence, you could export from the project panel to a video file and re-import it, and use that as a DL in Ae.

So the 1st pic is in pro and the 2nd pic is what it scales to in after.

Ive never ran into this problem before