are all LED lights like this? Do they all have a warm up time? I have a couple of Tri-Phase lights, and I want to switch (relay) them between other lights while I DJ, but they take a while to turn on. Can I do something in DMX mode?

no not all are like that. The tri phase when it is powered on goes through a self check mode wither in dmx or any other mode. It is checking the motors and the led PCB to ensure it works fine. Maybe think about buying a UC3 controller for them or program them in dmx mode.
Welcome to the forums.
Sincerely,