Hi
Your *own* words say that, even if one does a login and a logout during a game-day, if one logs in during a game-day, and if one continues logged in over the end of that game-day, that will re-set the quest ...
If you have already logged out once during the same day, the quest will not reset.
So someone who has done a login and logout, who then logs in again at 23:59, does some moves, and then logs out again at 00:05, will find that the quest resets itself ... and *that* is a problem !
The same rule applies, once you have done 1 login and 1 logout for the day, quest will not reset if you are online before 00:00 and logout after.