In a (speculative) word, politics.
They don't really detail this in the show because they quickly get into other plots, but it seems fairly simple. Babylon 5 was originally Earth Force property, under Earth Force command, and funded by Earth government. While it became an independent state, expectations back on Earth would probably have been that once questions of command, responsibility, and prosecution surrounding Sheridan's rebellion had been settled, that control of the station would have reverted back to Earth.
Except, no, surprise! We're announcing an Alliance, and we'd like to keep your stuff!
Cutting Earth out of the picture on such a straightforward concern would have been political suicide at that point, especially with all the other trouble they were stirring up. Promises of further tech or not, few would have believed their promises if they were willing to just take what they needed right off the bat. So on the books, Babylon 5 stayed an independent state so that Earth would be clear the Alliance was calling the shots there. Earth Force personnel, presuming they wanted to stay with Earth Force, would have been considered on loan, or inserted into the Interstellar Alliance chain of command (which I presume was the case with Lochley), and would probably have rotated in and out as needs demanded or tours and terms expired. The Alliance would have arranged payment for the physical property of Babylon 5 once all the bureaucratic terms had been hashed out so no one would have felt that Earth was shafted. Once it's all evened out it can be officially considered a state or outpost of the Alliance.
Politics can add spice, but this is largely boring gap-filler, so thus why I beleive it was never covered in-show.