The hot air is moved with some repurposed computer fans up high in a few doorways, and a return cold air fan , like your case, blowing the lower colder air back to the room with the mini split.
The introduction of the fan moving the cold air into that room has a FAR larger impact on the house temp than just the fans moving the heat alone. (They obviously help as well but it's far more effective to move the cold air).
As a geek side note, I also have a few "in wall" fans that direct into 6" vent work, and come out floor registers for the second floor. There are enabled or disabled via esphome temp sensors -- when a differential greater than X is noted, the fan(s) turn on, more rapidly evening the temps upstairs and downstairs.
(To be fair, I also have an oil hot air furnace, and a wood stove, but the furnace has not been used for 2 winters, and the wood stove on the cold cold days in Jan/Feb when the heat pump isn't very happy)