Logan and Jean have still only known each other a matter of days.

Knowing what we know about the government, do you really think it would have taken only days to set up a Department of Mutant Affairs with the kind of staff it would have needed/taken to do the Worthington research? I say at least a few months have passed between the second movie and this one, and it's conceivable that at least a few months have passed between the first movie and the second.