1210623-2005 EDT
I know nothing about your particular need.
However, think about it logically. How does a plain furnace or airconditioner work with a thermostat?
Consider heat. A simple thermostat senses temperature and has a two state output -- heat and don't heat. Modern thermostats do something internally to reduce hysteresis. I have a Honeywell thermostat and at the thermostat position in heating conditions, meaning that outside temperature is not too hot or too cold, so that the furnace cycles on and off, my temperature stays between 67.4 and 67.9 or within +/-0.25 degree F. This thermostat only directly controls the gas valve. A different sensor in the furnace controls the fan.
In your system you will have two thermostats, one for each zone. How do the dampers work? Are they just on-off, or are they proportional? This answer will make a big difference.
Suppose they are on-off. Then a thermostat for a zone needs to do two things. On request for heat open the damper, and also command the furnace to turn on. When the thermostat says off, then the furnace should turn off, but there is a lot of heat to still be dissipated and the damper should stay open until the blower turns off. The second zone should do the same thing independent of the first zone.
I suggest things are complicated by how you want the two dampers to operate when the heat periods for the two zones are not simultaneous but have overlap. Now turning off of a damper is more complex.
These comments are primarily to get you thinking about how this system is to work so you can ask more questions, and provide more information on what the system is to do..
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