I don't think we can say definitively that the Kelvin timeline was exactly the same as the Prime timeline right up to the appearance of the Narada in 2233. I believe that the Narada's arrival had a ripple effect both "uptime" (the flow of time into the future) and "downtime" (the flow of time from the past).
Let's keep in mind that the Kelvin timeline's James T. Kirk has had a very different life from what his Prime counterpart did. The Prime Kirk was a very prolific time traveler, as were future captains such as Picard and Janeway. If temporal incursions into times before 2233 that originate from times after 2233, then the timeline may have already been different before Narada's arrival. Or, to make it more complicated, that timeline did not exist until the Narada's arrival, and its past and future all occurred simultaneously to create the new universe.