I feel like those changes, where Starfleet ranks mirror the US Navy's ranks and traditions, were a TNG invention. I don't recall many ensigns in TOS, but TNG was the first place where we saw actual development and definition of ranks, as well as much closer examinations of the Academy itself. It's possible that things changed in terms of ranks between TOS and TNG.
Right, I do think there had been changes, but these mostly seemed like a fleshing out rather than wholesale changes. Ranks were added for instance, like Lt. Jg. There were ensigns in TOS, notably Chekov for one, and one is left with the impression that 0-1 (Ensign, 2nd Lt.) is the rank you graduate with and is the rank that Chekov graduated with.
Who knows what JJ&Co were doing with their conception of the Academy or officer ranks, etc. They even had a doctor going to the Academy. In the JJAltVerse god only knows. Maybe you can be an 18yo Admiral. It seems like they just made things up as they went along, and it didnt matter if it made any sense whatsoever.
Ever heard of OCS or OTS? People with degrees dont go to the Academy. Thats why it takes 4 years, you are getting a Bachelors degree. If you already have one (in todays world) you dont go to the Academy (you already took English 101, Intro to Philosophy, etc) so you go straight to officer candidate school. That only takes a matter of months, and presto, you are an Ensign/2nd Lt)
So to rationalize JJAcademy, we will just say its an amalgamation of the traditional Academy (4 year degree for HS grads), OCS/OTS (the military portion of your training for people who already have the Academic bachelors), specialized training and degrees for those with advanced civilian training (doctors, nurses lawyers, etc) and any specialized schools associated with the various MOS' and Rates.
One vast Academy, and on the grounds of which all the usual training takes place. Heck, we can even throw in that enlisted boot camps and the various schools for THEIR rates/mos are also located there.
That would be one huge campus, but what the hell. that still doesnt explain everything you might see in JJAltVerse, but thats the best I can do.