I'm guessing that the color in the Illustrator document wasn't a solid color but was a gradient. Gradients aren't preserved in the conversion to shape layers.
Show us a screenshot of exactly where you're trying to modify the colors of the extruded shape layers.
Ahhh. That would explain it. The color is a gradient.
If the Illustrator document has the components in indivdual layers (not groups: real layers), you can import the document into AE as a comp and animate each layer in 3D space.
If there is just ONE layer, well, you can fix that in Illustrator.
Is there any way to cheat a gradient with the Ray Traced Rederer? Or am I stuck with solid colors?
I can only think of one: make that logo far larger than it is now to preserve the resolution and turn it into a bitmap. I hope someone wiser in the ways of Illustrator has a better idea.
Can you flatten the groups in a given layer in Illustrator so AE doesn't see the gradients, but just a layer? Aah, that's probably just a Photoshop thing.....