I had the same situation once, airbrushing lacquer paint. When I finished I gave the paint one full day to dry, then when pulling the tape the paint stayed firmly attached to the finish, but paint slid right off the tape.
Now when using any lacquer like Alclad, I just wait for a few minutes then pull the tape. In the case of the paint not sticking on the tape, I used the blue polyurethane type. By not waiting long now, the paint seems still soft enough to remain adhered to the tape. No problems since