I unexpectedly had a stay this weekend at a Hyatt Place a day after checking out from another reservation that hit my 20 night milestone. I went into my account, selected the 2k next stay bonus after I'd checked into the Hyatt Place (but before check out) and saw the 2k points post in line with the points from the stay. So it seems as long as you pick the milestone benefit before check out, it will apply to that stay.