A different future

As James Mangold explained, Logan takes place in the future. However, this is a different future from the one in which the rest of the X-Men have lived (the one in which Apocalypse arrived), being set in the Days of Future Past timeline. So, in a way, Logan is set in an alternate reality, one in which Professor X didn't seek the younger versions of the X-Men, as promised to Wolverine in Days of Future Past.

If it’s a bit complicated to understand at this point, it’s because we don't have all the details about the film. But it isn't as if the X-Universe timeline weren't a mess already.

So I can say that Apocalypse didn't arrive for Logan in the form of the all-powerful ancient mutant, but in another way. I can say that after he was retrieved from Potomac, something else happened, which led to the extinction (I presume) of all mutants.

It remains for some of the details to be clarified. Maybe it can all be explained through the whole time-ripple effect that Beast/Hank McCoy was talking about in Days of Future Past "“ if it wasn't the Sentinels that brought the destruction of the mutants, it was something else"¦