DS9 and VOY are spin offs of TNG, and TNG is a spin off to TOS. And in some ways, they are sequels. The DS9 pilot clearly continues Best of Both Worlds and other TNG episodes featuring Cardassians and Bajorans. With Worf's appearance, the 4th season turned into a sequel to Generations. With the Defiant and Worf appearing in First Contact, the movie became a direct sequel to DS9, and when the attack of the Borg was mentioned again in one of the episodes, DS9 became a sequel to First Contact. Same goes for Voyager. There are many intersections between the shows.
And when Scotty in his uniform from Star Trek 6 walked onto the bridge from TOS, or when Sisko met Kirk on the bridge of the Enterprise, when Tuvok had a flashback of his time aboard the Excelsior, and when Picard buried Kirk, both the TOS movie era and the TV show were officially recognized as prequels to the TNG/DS9/VOY story.
All these shows are clearly in the same universe, telling the same ongoing story. I am using "sequel" as an equivalent to "continuation", though.
But there's no such connection in the new movie, neither to TOS nor to TNG. Spock Prime might come from the Mirror Universe from all we know. He might come from a universe where the Enterprise looked exactly like she looked in the new alternate universe (which she clearly didn't: Scotty in TNG on the TOS bridge, and Sisko & Co walking through the Enterprise's corridors in DS9 are the fictional evidence of that). He might also come from a universe where Kirk became Captain right after the Academy (which is why he is surprised about how Kirk was not Captain of the Enterprise).