(Will also submit bug report, posting here for visibility.)
When you import an .ai file, if the bezier handles of the contents of any layer go outside the dimensions of the layer itself, AE treats the bezier handles as part of the layer, for size purposes. Effectively, this means any precomps created with the layers will be too big, and the center point is offset to what it really should be.
In AI, add more vertices to you shape path
Object > Path > Add Anchor Points
Repeat until no handles go past layer edges
In AE, precomp your too-big layer, and use a comp cropping tool to shrink the layer to the right size, and another to reset the anchor point.