Originally Posted by Quark
I don't think transwarp beaming is mentioned ever in Star Trek before the 09 film. At the same time, it could have happened between Scotty's time on the Enterprise-B and before his accident on the Jenolan.
He could have developed it after the Jenolan. With all that free time he could easily sit back and pick up on old theories that he might have been working on prior to the ship's disappearance. It's never actually established in the movie that transwarp beaming was ever actually done in the prime timeline prior to Spock Prime's encounter with Nero. The only thing that is established is that at some point in time, Scotty had been working on a theory about transwarp beaming, including the mathematical formulas. Exactly how long he was working on it is up for speculation. It could easily have been something that he had been working on as a junior officer then shelved and then picked up again years or decades later. Spock's knowledge of the formulas could simply be a result of him reviewing Scotty's work during peer review in the prime timeline. Spock might have been assisting Scotty with the theory prior to the events in the movie. The scene in the movie might very well have been the very first test of the finalized theory.
But yeah, with Tomorrow is Yesterday, you're talking about a 1st season episode. You're going to have a lot of plot blatant plot devices floating around. I'll have to pull out my dvds and watch that episode again but for now I'm going to take Futurguy's interpretation of the events in that episode. TNG seems to suggest that transporting from a ship in warp is probably not done regularly if at all. The episode "The Schizoid Man" they use near-warp transport where the ships drops out of warp and then jumps back to warp just as the subject being transported is in the rematerialization phase.