DIAGNOSIS The Nest E didn't correctly detect your dual-fuel or heat pump with aux heat system during its initial wiring scan. It probably has your auxiliary heat wires (often labeled W2 or AUX) plugged in, but it's configured in the settings as a conventional gas furnace system.
FIX You need to manually change the equipment setup. 1) On the thermostat, go to Settings > Equipment. 2) Go through the setup prompts again. When it asks for your fuel type, select "Electric" if you have a heat pump. 3) It will then ask what wires are connected. Make sure you tell it you have both "O/B" (for the heat pump reversing valve) and "W2/AUX" (for your backup electric heat strips). This is the critical step it likely missed. 4) Complete the setup. It should now correctly stage your heat pump first, then use aux heat only when there's a big temperature gap.
IF THAT DIDN'T WORK Double-check the physical wiring at your air handler/furnace. The wire connected to 'W2' or 'AUX' at the Nest base must go to the terminal for the auxiliary heat strips on your HVAC control board, not to a generic 'W' terminal for a gas furnace.
HEADS UP If this is set wrong, your system can run very inefficiently. The worst-case scenario is it could run your expensive electric aux heat strips at the same time as your heat pump, which is wasteful and can overload some systems. Getting this configuration right is key for both comfort and your power bill.