You NEED the manual for the color head.
If all the power to the head is via a single standard power cord to the timer, the fan will NOT run except when the timer is ON.
For the fan to run w/o the timer on, the power to the fan has to bypass the timer.
The wiring can be a little complicated which is why you need to get a copy of the manual for the color head.
Example, the Omega color head has a 6 pin power cable that has to go to a special power supply where the timer is on a separate circuit from the fan.

What make and model is the timer?
Maybe we can find the instruction manual on line.