A viewpoint from the outside.
Kevin Garnett has always been a player necessitating emotional support for the very reason that he assumes so much responsibility for the performance of the team as a whole. He did this also pre-Boston.
I think that the rock-strewn road that the Celtics took during the playoffs weighed much more heavily on Garnett, than on the other players. The expectations for Boston, in view of their regular season record was certainly a heavy load to carry for one tending to shoulder these things unconsciously by himself. The possibility (real or imagined) that the road to the Finals could have been interrupted, after all of this expectation, must have been exhausting.
However, psychologically, I think that now that the Team has arrived to the Finals, now that the peril of being eliminated before getting there has been avoided, well, a large portion of this weight can now be removed. So, his reaction is certainly understandable. It is that of a person who has just removed a large part of this unsustainable weight. I think that now that the goal has been gained, the Finals, that Garnett will recharge the batteries and play more relaxed.