[Vitaly Tomachevski]

I was having a similar issue. My colors were not matching from Illustrator to After Effects while using ai files. Until I tried this.

In Illustrator,
First turn all of you Spot colors to Process colors.
Next, Go to File – Document Color Mode and select RGB Color.
Then, Go to Edit – Assign Profile and select a profile.
(For example: sRGB IEC61966-21)

Make sure that in After Effects you set the same color profile as in Illustrator by going to File – Project Settings – and selecting a working space profile
(For example: sRGB IEC61966-21)

When you are about to render and select add to render que, Go to Output Module – Color Management tab and select an output profile you wish to convert the colors to such as sRGB IEC61966-21.

Hope this helps.