I still have the current game saved after the spies, but not before. And yes they are still there many turns after the CEC.
I think it may be because the AI takes it's turn (everything except ships) at the same time you are working on your turn. So before you placed the CEC, an AI got spies qued to go on those tiles.
I have noticed that before. I will see and neutralize a spy, then when I hit the next turn, I will see the announcement that one has been located. Similar to attacking someone and then seeing the declaration of war on the next turn. But if they dropped 4 spies RIGHT before I built the CEC, they got awfully lucky...