To me, the secret ingredient in the recipe or whatever metaphor you want to use is the trade for Al Horford. He not only was able to come in and shore up our greatest weakness in the core rotation (PF) he has actually made it into a strength of the team. There have been a lot of players that have improved (Tatum, Brown, Smart, RWill, GWill). But for all of them it feels like just kind of normal expected player development. Ainge picked them, Stevens developed them for several years, Udoka seems to have taken them even further. I feel it is the players that deserve the most credit for this.
But even accepting that Horford has been an important addition, I am not sure how much of the foundation laying for the trade was done by Ainge before the official reorg was implemented. The trade happen really soon after. I guess even if Ainge was involved, clearly Stevens liked the trade and got it done so credit to him.