You need to clarify your post. From your description, you may have Roof AC Heat Pumps. AND from your description about the Emerson wall Tstat.
1. It is possible that the Emerson is wired to the LP furnace
2. It is also possible someone added the Emerson to bypass/inline with the BLACK square wall tstat that controls the roof AC/HP.
3. You need to state brand and model of Roof AC/HP.
4. You need to clarify from your FIRST description of Heat that the heat came out of the FLOOR registers or from the roof AC registers.
5. You stated HEAT and DOWNSTAIRS Air----No such thing on your model. I don't believe FR installs a Basement AC on any of their product line.
6. IF Dometic wall tstat and the Tstat Fan is set to LO or Hi, then when the furnace is ON, the roof ASC fan will run. Doug