Mini-split and vent on same puck?

I have central heat system throughout house. Two upstairs bedrooms heat very quickly and overheat. The master bedroom, downstairs, is too cold in winter and sometimes too hot in summer.

I currently use an ecobee. 

My vision is to put vents in the two upstairs bedrooms and have sensor pucks there. Also put vents downstairs, in living room (with an ecobee sensor) and dining room (where ecobee thermostat is located). And in master bedroom install a mini-split heat pump and a smart vent with flair with a puck set up as a gateway. (In all other rooms of the house I typically have the vents closed all of the time.)

I am unclear how and if a single puck would control a vent and a mini-split, and also unclear if I can set up the minisplit to cool even though my central system has no cooling.