Imported Illustrator File Produces Offset Motion Path

The default anchor point for a shape layer in 0, 0 because the layer has no size until you add something to it. It is the same thing with Text layers.

When you convert a Vector file to a shape layer has dimensions and the anchor point is half the width and height of the new shape layer.

To get the motion path to line up properly add a null to the composition at the default comp center, then Parent the moving layer to the null and reset the null's position to 0, 0.  If you have not transformed the shape layer in any way before copying the vector path to a shape layer, the motion path will now line up. 

Another option is to use the Create Nulls From Paths.jsx script and select the path and Trace Path. This will create a null that follows the selected path no matter where it is or how the layer with the path is transformed. Then you can just Shift + Parent the layer you want to move to the Null. That is the workflow that I use most of the time. The only caveat is that the path must not be in a Group that has transformations applied. That will throw off the position calculations.

There is a third option. If you have XD, you can open an Illustrator File in XD, select everything, then use the File/Export/After Effects menu option. This will create an After Effects composition with every object in an AI file as a shape layer, all text layers as editable text, and all groups as Nested comps with one click.