I think it started in earnest the day of his AMA, whenever that was.
It actually started long before that. Fuck U Spez was already a meme when all of the API/third-party app stuff took off, but at that point, it was still mostly a holdover from previous examples of Spez being a shithead. The thing that really gave it (new) life was that AMA.
In my experience, the existing lemmy servers really started taking off from the dozens of active users that were there into the hundreds, with each day after May 31 having exponential growth. By the time Lemmy.world started around June 17, we were into the thousands. This was a huge change many of the users and admins weren't expecting, and the servers were barely ready for.