My copy of BtS seems to be rather... bipolar.
I'll get a green message saying my spy was caught, but he'll return to my city. And I'll get a red message saying an enemy spy was caught within my borders, but he still succeeds in hurting me somehow.

Anyone else get this slightly amusing bug?

Well if the spy returns to your city, that is a good thing right. That means he/she escaped and can be used again. I think green is appropriate here.
Same logic for the second case. The damage is done so it should be red.

But if a spy is caught, shouldn't they do no damage and vanish?

Depends on whether or not he/she succeeded in his or her mission before or after being cought. Your bug is quite amusing though :)