That's because While X-Men: First Class took place in the '60s and X-Men: First Class is based in the '70s (but takes place all over time because, well, time-travel is a thing in the X-Men movies now), X-Men: Apocalypse will take place in the 1980s.
"We’re going to deal with the notion of ancient mutants – the fact they were born and existed thousands of years ago," Singer told Collider. "But it’ll be a contemporary movie – well, it’ll take place in the ’80s… The ’80s is a period now – it’s hard for me to believe that!"
It seems that, contrary to fan theories, X-Men: Days of Future Past will not end with Singer retconning the first three X-Men films out of existence and ushering in a new era for the team. He's making connective tissue that will link X-Men: First Class with X-Men, here, and the closest we'll get to reboot territory, apparently, is younger versions of familiar characters (presumably some of those first introduced in the original 2000 film, which he directed).
Oh, and he wants to blow a lot of stuff up, too.
"Apocalypse will have more of the mass destruction that X-Men films, to date, have not relied upon. There’s definitely now a character and a story that allow room for that kind of spectacle," Singer explained. "I don’t want to get too specific, but we’ll introduce familiar characters in a younger time. That’ll be fun to show the audience. I call these movies in-between-quels. It’s a mind-f--k sometimes in terms of where things fall in the timeline!"