well its not a reboot. A reboot completely disregards everything from before and starts new from scratch.
I'm pretty sure he remembered what happened in DOFP and before DOFP. He time-traveled but nothing from his memory during the trip was wiped out. Like Shadowcat said, he was gonna be the only person that will remember what happened in the bad future.
So its not really a reboot. Its not even the same thing with Star Trek. Because with Star Trek 11, the events of the Star Trek 6 and the last Star trek Generation film didn't lead to an alternate timeline where the characters of Chris Pine/Zachary Quinto exist.
It is still not a reboot. As future X-Men movies are still connected to the previous X-Men movies. A reboot is something like The Amazing Spider-Man, totally no connection to the previous Spider-Man movies directed by Sam Raimi or The Dark Knight trilogy. Websites aren't calling X-Men: Apocalypse as the 2nd film of the series, right? It is still the 9th film in the series (8th, if you don't count Deadpool).
If this were a direct continuation of the previous films, it wouldn't have erased the events of the X-trilogy or the Wolverine films and X-men: Apocalypse wouldn't be contradicting those same events so that, by itself, makes DOFP a reboot.
DOFP is a direct continuation of First Class, so you are wrong in that regard. Nothing from First Class was erased. Apocalypse will be the third film chronologically in this continuity. These are not reebots
DOFP is also a direct continuation of X3: The Last Stand and The Wolverine but the ending of DOFP completely erases those movies along with Origins, X1, and X2. The definition of reboot is to discard all continuity in an established series in order to recreate its characters, timeline, and backstory from the beginning and if you are going to make a movie with the sole purpose of erasing the previous installments that came before it, then your ARE making a reboot which means that it is you who is wrong.
And DoFP didn't do that. At all.
DOFP is also a direct continuation of X3: The Last Stand and The Wolverine but the ending of DOFP completely erases those movies along with Origins, X1, and X2. The definition of reboot is to discard all continuity in an established series in order to recreate its characters, timeline, and backstory from the beginning and if you are going to make a movie with the sole purpose of erasing the previous installments that came before it, then your ARE making a reboot which means that it is you who is wrong.