Are the lights installed in a venue or are they for a mobile application?
When you say breaker, do you mean something like in the wall panel of a back room/basement/garage? Or some type of strip surge?
In general, intelligent lights, and your lights specifically cannot be powerd off via DMX/Analog control. Like you said, you can turn the lamps off, but the fan will still run until the unit is unplugged, or switched off via some other means (wall switch, breaker panel, strip surge switch, etc).
Let me know, and I give you some more advice.
Best,
-Tech