If we assume that the monster that the arrow is fired at takes a turn to kill (not a bricko monster), that the next adventure is adventure.php, and that no shenanigans are done with non-adventure.php areas to make things more complicated (in other words, the simplest scenario), the counter after firing the arrow should be 1 larger than when the monsters show up later, since the later arrivals set the counter on the turn they show up rather than on a later turn.
For the second (or third with equipment) wandering arrowed monster, counters shouldn't be created any more, ideally.