Of course, Worf in Parallels thought he was in the same universe at first. Alot would be the same among any number of an infinite number of parallel, quantum, alternate timelines.
Technically, he was. They were just splits of his original timeline.
Parallel and divergent timelines are two distinct things in the Trek world.
Personally, I'm more curious as to how the Mirror Universe came about. Can we see a Mirror Universe Nu-Trek with MACOs and an investigation by Temporal Investigations to correct everything?
Also, revisit the ending of the Temporal Cold War.
Well in the case of Worf, Spock in ST09, and the Mirror universe, the characters experience alternate timelines that already existed prior to their arrival in them. Their arrival doesn't create it. Although maybe in the Orci model, still more alternate timelines were created by them.
Personally, I hope we never see the Nu Mirror.