Not sure about wiring of your system, but some have a relay to prevent the AC from operating at the same time furnace.
Furnace should provide it's own power and relies on a contact closure for operation from the thermostat.
Looks like contacts are in control unit. Have you checked the mode functions in the zone for furnace operation?
From manual:
If a furnace is operated by the Comfort Control Center, the thermostat wires are attached to the two (2) blue wires from the control box. The furnace dip switch for that zone (control box or power module) is turned on