A couple of notes about setting up Illustrator files for After Effects:
1) Design with RGB color is always a good idea.
2) Make sure that the paths you want to animate separately are in new Layers
3) Your footage will usually come in using the duration of the last comp you created. It looks like the layers you've imported think that they are a sequence of frames (this can happen when you version out your files Illustration_v1.ai,Illustration_v2.ai, Illustration_v3.ai...)
At the bottom of your import footage dialogue box, turn OFF the sequence options.
4) You should be able to import your entire .Ai file as a Composition. If you use "Layer Size" dimensions, your layers will each have centered anchor points.