In the new rules, carried figures cannot perform any actions (other than free ones) until their next turn.

Does this apply to characters moved via TK?

Wizkids hasn't said anything to stop this. It's believed that they will but for now I believe that it can be done.

I don't believe there's been any indication that TK is going to be limited in this way, actually. A TKed figure is still able to act, and I have not seen anything to suggest this will change.