I think the key for Bud is he is making adjustments, which he didn't do in the playoffs for the last two years.

Some of it may also be Holiday. Not yesterday, but in game 3 Holiday had the ball moving up the side and Giannis was going up the middle of the court. Giannis called for the ball, and Holiday waved him off, telling him to go to the low block.
That is a huge difference from the past couple years where Giannis would want to bring the ball up and run into the defensive wall.

Bud / Holiday have gotten Giannis to buy in that he can make more of an impact when not dribbling the ball up court.