If you watch X-Men Origins: Wolverine and then watch The Wolverine, you can find an incongruency in Wolverine's story. In X-Men Origins, you can see that in the World War II scene, Wolverine and Victor fight in Normandy. In The Wolverine, he is a prisoner of war in Japan. What happened? Both movies were made before Days of Future Past.
Actually there's no incongruency.
The Normandy landings happened in June 1944, the atomic bombings in August 1945. Unless I'm forgetting The Wolverine stating Logan was a prisoner for a very long time, it's not unreasonable to think he could have been in both theaters.
It's certainly not explicitely explained, but time-wise, it's not physically impossible.