No, it was not a main reason
While the situation with Ahsoka certainly did impact him in ways that may have been a factor in his decision to betray the Jedi, the actual turn itself really boiled down to a single moment: his choice to save Palpatine, and for sole purpose of saving Padmé.
One of the primary plot elements of "Star Wars: Episode III" is the reason why Anakin makes the turn to become Darth Vader, which from a story perspective means that the viewer needs all the information necessary to understand and accept that choice. All throughout the movie, we witness his frequent dreams of Padmé dying and the fear that it brings him. The Jedi give him answers he doesn't want to hear, and when confiding in Palpatine, the chancellor reveals that there may be a way to save his wife (and in doing so admits that he is a Sith lord).
Anakin, still bound by his loyalty to the Jedi, decides to warn the council. What he assumed would be an arrest ends up turning into a fight that leaves only Mace and Palpatine standing, with Anakin on the sidelines as the deciding factor. Palpatine uses this opportunity to specifically focus on and take advantage Anakin's fear of losing Padmé, and it is for this reason that he makes his choice.
Could the way the Jedi council treated Ahsoka have been something he considered as a reason for turning on them? Probably, just as we can certainly say that his own feelings of betrayal by the council (for not granting him the title of Jedi Master) were all considered. All of this on top of the situation at hand, with Palpatine "calling for mercy" and Mace not having any of it.
But all of these were mere ripples to the wave of fear that was the loss of Padmé. While he does claim that "It is not the Jedi way", this was more likely his trying to justify keeping Palpatine alive (the last thing Anakin says before doing the deed was "I need him"). It was for that reason that he chose the path to the dark side, to follow Palpatine and learn from him of how she might be saved (as he says afterwards: "I will do whatever you ask...just help me save Padmé's life. I can't live without her.").
Here's the clip of his choice and subsequent turn: