It didn't really. Days of Future Past overwrote itself at the end of that movie. In the rewritten timeline, the future that would lead to Logan was just that Xavier's school was still open and active and Jean and Scott never died. No other info about the outside world was shown. All that was true in Logan's history, too, until Xavier's illness accidentally killed everyone at the school.
And if the Tarantino movie is a darker or riskier take (which would be logical, though not guaranteed), it wouldn't make much sense to use the same cast.