I saw a heat pump system today with no setting or indicator light on the thermostat for emergency heat. The system is less than two years old.
There is a 60 amp breaker in the panel labeled "heat". Access to the air handler in the attic is horrendous, but I also saw a 60 amp disconnect there.

Does it sound like the wrong thermostat was used, or what?

The outside temp today was about 75, and when I turned the thermostat up to 80 the outside unit kicked on and produced warm air. When I changed it over to AC it worked great. It's an electronic thermostat, so there are no dual mercury switches to look at.