Installing/swapping Coleman Mach thermostat in my RV

Our new home thermostat is a digital Honeywell and it clicks as the temperature reaches the set point. Say it's 90 in the coach, you want 80 so you select A/C (vs Heat) and move the temp control toward 80. By "move" I mean Slide if Analog, Push Button if Digital). As the set point approaches 80, it'll click to start the system. Once it IS 80, it'll click again to stop the system. "System" being Fan and Compressor if that's how it's set up (Auto Fan), or Compressor only (set up for Fan On).