Transfer Illustrate files to After Effects in seperate layers

It looks like the Illustrator file has multiple artboards. That is the first mistake. If you want to fix it, you must have Illustrator installed. The first step is ensuring that the Document Settings are in pixels or points. The second step is to check the size of the Artboards. The third would be to go to the Layers panel and see if you can make sense of the layers. The end goal is to have every element you want to animate on a separate layer. If there was some planning and grouping, you might be able to get away using Release To Layers Sequence in the Layer Panel Menu and then dragging all of the new layers that were created when you Released to Layers above the original first layer. If there is no planning, you will have to make a bunch of new layers, then drag objects into the appropriate layer using the Layer Panel. 

The last step would be to do a Save As and carefully check the Save options. It will look like this:

If you do not have Illustrator, you will have to send the project back to your designer or hire someone to do it for you. The fix could take 2 minutes or 2 hours. 

* The "Drag & Drop here..." area works, but it is a pain for the forum users to access the photos. Please do not use it to share images. You can use the toolbar, drag your pictures to the reply field, or even copy and paste the file directly in the reply field, then size them up so we can easily see them.

I'd make sure first that you're importing the footage as a composition. When you're importing make sure that you choose composition in the import window and the 2nd window as the graphic is coming in.

Also, if the footage is in your timeline you can select it and go to the top of the interface and go to layer/create/convert to layered comp.

If the footage is try flat then you'd need to separate the layers in Illustrator.