Hey there,
I am really sorry for the delay of this reply as it is a weekend for us here.
Basically when the user click on this filter 'Sort by Recently Logged In' (
http://take.ms/vkOeI) under member listing page, the system will always check on site regarding those existing user when is their last login date time.
For example :
User A - This user logged in on the site at 3pm.
User B - This user logged in on the site at 4pm.
User C - This user logged in on the site at 5pm.
If they never login again, this recently logged in sorting result will always show User C, User B, User A.
If User A login on the site today, so the sorting result will become UserA, UserC, UserB.