I thought with dual-fuel the gas burner & heat pump were never running at the same time, since the incoming air from the heat pump coil into the gas burner's heat exchanger would be too high(?). The higher incoming air temp leads to lower heat exchange efficiency on the gas burner (especially if condensing) and going overtemp on the heat exchanger. This isn't a problem for resistance auxiliary heat strips (which can operate safely and at the same efficiency at any incoming air temperature and can easily be modulated), but a complicated control issue for combustion equipment.
Many 2- stage gas furnaces use a simple (sometimes programmable, sometimes not) timer to determine when to kick up to the high stage, with no direct thermostat control of the second stage.
Without so much as a model number it's impossible to take more than a WAG at the control scheme and thermostat compatibility. It's sort of like asking "What type of fuel injection controls do I need for my hybrid car?".