I talked to the guy that installed the unit... He said I don't need a dual fuel stat... He said he phased them together (Transformers) so it would not as you said buck so should work... Does this sound right...
He apparently doesn't know what a dual fuel thermostat or dual fuel control does.
If he phased them (yes, it is possible) then you wouldn't have seen smoke. So he probably did that wrong also.
its an isolation relay that is used to prevent transformers from bucking each other. And most thermostats have that built into them for many many years now.
A dual fuel thermostat prevents the furnace and heat pump from running at the same time. Other then during defrost. And can also be set to lock out the heat pump at X temp and make the furnace only run instead.
You need a dual fuel thermostat or control. Or, a lock relay system made up for it.