When using the CSA TA can you give a character an action token after they have already moved?
For example:
Say Deathstroke had already moved, now can a CSA member give him the action token to use the team ability?

I think so yes...
Even if the CSA TA gives a token, it is still a free action, and should therefore be possible to use after another tokenable action. I seem to remember talk about using the CSA TA to push figs off activation clicks on turn 1, which adds some strength to my view...
But if anyone feels I'm wrong, please correct me.

No you're right. Of course the fig taking the second token will take a click of pushing damage, barring Willpower of Power Cosmic TA.