So like Back to the Future?
Yep. The events of Back To The Future had Marty create an alternated reality where his dad wasn't a loser but in fact an author.
Marty will have memories of his old life but everyone else will have memories of this new Reality.
Essentially Marty has no memories of his current Parents and siblings as they lived a different life to him..
The funny thing with time-travel is that Marty and Wolverine will have memories of their reality, but they'll be living in a new and different reality. They'll be interacting with friends and family who in fact knew alternate Marty's and Wolverine's.
It raises the question what happened to the Marty and Wolverine who existed alongside this new reality?
Marty 2 would have been raised by his Author dad and Logan 2 would've been an X-Men through different circumstances, but as of the moment Marty 1 and Logan 1 went "Back" to the future they essentially replaced those versions.
Goes like this:
Marty is raised by his loser Father. He goes back in time and creates a new reality. George grows up differently in this new reality, he marries Lorraine, becomes author, and has children who he raises. He spawns Marty 2 who grows up with this family.
Original Marty returns to 1985 and sees Marty 2 go back in time. Marty 1 then resumes his life by taking the place of Marty 2.
Essentially the same thing happens in DOFP.
1970s Logan has his mind trans-placed with 2023 Wolverine through mind time-travel.
1970s Logan remains locked in limbo by Kitty Pryde while Wolverine (2023) faffs about changing history in the seventies
When Wolverine (2023) and Logan (70s) switch back, Logan (70s) has no memory of what Wolverine was doing whilst in this body. He goes on with his life. A new reality is spawned.
Logan eventually goes on to get Adamantium on his bones and joins the X-Men through currently unknown means, he ages with the team, going on adventures and so on.
Wolverine (2023) goes back to the future, this new alternate reality future and essentially overwrites (70s) Wolverine and takes his place.
All others would have been teammates with (70s) Wolverine not "our" (alternate 2023) Wolverine.