The way I see it, everytime the history of Earth 0 is changed, a new parallel earth (or several) is spawned that mirrors the erased history.
So Earth 0 originally had Superman showing up in 1938. Then history changes such that Earth 0 has Superman showing up in 1956. But at the same time, a new parallel earth, that comes to be known as Earth 2, is created which has a version of the 1938 Superman.
This does mean that logically there are earths out there with versions of the Silver Age Superman, the Byrne Superman, Birthright Superman etc. Which is borne out by Convergence. Which in turn explains exactly what happened in Superman Reborn.
Basically, in Superman Reborn, the pre-Flashpoint Superman is Superman from an earth that reflects Earth 0 Superman's timeline before Manhattan tampered with it to make him the New 52 Superman. When he merges with the New 52 Superman, it brings Earth 0 Superman's history closer to the pre-Mahattan version. In a way that's what all the continuity changes since Wally West's return has done.
Incidentially, I suppose Johns has now given an 'official' answer to a long-standing question of when exactly did the Golden Age Superman become the Silver Age Superman. The cut-off date is apparently 1956. Of course, Superman's history probably 'slid forward' once more to account for the Bronze Age Superman - probably to the early 1970's or so.
.