I have only seen the CS AI traffic when I fly the F-4 at 12 o'clock flight. I have never seen them at any of the airports where I shoot down the Civilian AI (GA and Airliners) aircraft.

The first time I flew the F-4 flight I couldn't find the CS AI aircraft either. To find them, I turned on Show aircraft labels in Options > Settings > Display > Traffic tab. Since then I have learned how to find them using the radar in the F/A-18.
Another way to help you find the AI, when you first start the F-4 at 12 o'clock flight, is to climb a couple of thousand feet to clear the cloud/fog that you are flying in.

Hope this helps.

Mark