Some thermostats are more sophisticated than others. With the proper stat, and an outdoor sensor, the stat can determine when to add aux heat or use it exclusively.

If your stat doesn't have this capability, the contractor can set the stat's lockout temperatures to achieve the above. This is based on economic considerations and the capability of your unit.

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Most systems that don't have super-sophisticated controls, the indoor thermostat triggers the auxiliary if the room temp drops 2°F or so below the setpoint ... or if the thermostat is electronic (but still not super-sophisticated), it may activate the auxiliary based on run-time, if the compressor is running and the room temp isn't rising to the setpoint fast enough.

"Auxiliary" by definition runs the heat strip concurrent with the compressor. The compressor doesn't shut off, the heat strip supplements it. "Emergency" heat, on the other hand, does run the heat strip(s) exclusively, with the compressor being shut off, this is primarily in case of compressor failure. "Auxiliary" and "emergency" both use the heat strips, just different terms and usage intents. The auxiliary also runs during defrost, during which the heat pump reverses back to air conditioning to heat up the outdoor coils and melt off accumulated frost. The heat strips running during defrost have nothing to do with melting the frost, they're turned on to counteract the cold "air conditioned" air that would otherwise be blowing in the house.

A sophisticated control system with outdoor temp sensors can switchover to the auxiliary and lock-out the compressor at very low outdoor temps ... and likewise lock-out the auxiliary so it can't run (except during defrost) until the outdoor temp drops to a specified point regardless of how far-off the room temp is from the thermostat setpoint.

Another good post, dadoes.

I have to add that the strips can be activated in stages also depending again on your thermostat. So in mild winter temps the system would run the heat pump solely and activate one set of strips for a little additional boost at night or as the temps drop through the winter. As the temps drop further the stat can either lock out the heat pump and run both sets of strips (same as emergency mode) or run the heat pump with all available strips.
I do not recommend any system running the heat pump and all the available strips as it is counter productive. For example, The strips alone should be able to heat the home with no problem and say consume 20kw.. But if the heat pump is running and just needs a little boost and the strips are called in all at once then suddenly your consumption is 20kw+ the heat pumps consumption.
The best bang for your buck is to run the pump... if it can't quite keep up then one set of strips for a boost.. if it gets to the point more is needed than the pump automatically shuts down and all of the strips run. The stats with outdoor temp sensing and low temp heat pump cutout are great for them nights it drops below the setpoint say 20 degrees for a few hours and then warms back up. If its above your set cutout temp the heat pump runs... if its below, the strips run and the pump stays off. It will save in your wallet and wear and tear on your heat pump on the days/nights you might forget to turn the stat in emergency mode and its very cold.