Hey Rach!
This was exactly my experience when I adopted my dog Rocket. For the first couple of weeks, he was very calm and social with both people and other dogs. But then, after that initial adjustment, I started noticing the reactivity. He began barking at dogs on walks and he was also suddenly snapping at people too. It was in that moment that I reached out for help from a professional dog trainer.
So, yes, for Rocket at least, the 3-3-3 rule was pretty much spot on! Every dog is different, but I think those first couple of weeks are when you see the most surprising changes