The CTIS and fan air do share a common source, the wet tank. Air for both must make it through the protection valve, that 'regulator' looking thing on the rear side of the wet tank. So if air is lost in the CTIS then the wet tank will deplete and the fan turns on.
Because the Protection Valve is in line, the wet tank only has to drop to 70 or 80 psi to turn off the air supply to ctis and fan (not priority circuits).
A guage on the wet tank is a great diagnostic tool. Hint, a 't' fitting at the tank can provide a place for an air quick coupler, into which a test gauge can be plugged. If you install NPT swivel fittings you can do future work on that pipe/fitting assembly with much less pain.
On the discrepancy of operation between front and rear systems, a bad Quick Release Valve can do that. If one is bad, the front and rear dump air at different rates and retain different pressures. When 'dump' mode ends, the system tries to read pressure but the front and rear are equalizing through the wheel valves and the pressure is changing. The CTIS won't like the changing pressure and tries again. This continues and a lot of air is wasted.
Thats my understanding anyway.
Being a cold morning is a strong hint. A CTIS air seal in one of the axles may be prone to leak when cold.