Most mini-splits I've installed don't have a differentiating day/night thermostat, which to me is a must. So i power them up(must have auto-restart ability obviously) via contactor and plug the trigger cord into a controller. Window bangers usually don't either so I'll power them up the same way.
Dehus', I just set it to 50-55 and plug into it's own circuit. No need to plug into enviro controller imo, unless you just want it on at night time. If that's the case I'll power it up via contactor and plug the trigger cable into the night output on the enviro controller.
Pretty much the only thing I'll plug into and use the power available directly through an enviro controller are intake/exhaust fans, and a co2 controller if the enviro controller doesn't have a c02 sniffer.