Stars matter why? Because of the referees or because of their game? Because if it is because of their game a good coach can neutralize that.
Enter Popovich. That is why he has been so successful in the playoffs without winning the regular season derby.
Eh ... Popovich has been successful in the playoffs while also regularly winning the regular season derby.
The Spurs have won with ball movement in recent years, it's true. But they still have stars. Kawhi is one of the best young players in the league. Tim Duncan is still an elite player even at 38.
To answer your first question, yes, it's because of both. Stars are able to continue coming up big even though the game is called differently (allowing more physical play) and even though the other team gets to gameplan extensively to stop them.