Reactions I have seen classified as immediate in terms of when they occur. Such as, the man turned to run but in doing so, it immediately triggered the opportunity attack in that less-than-second gap of time. If multiple actions were to occur, I imagine that order of initiative would come into play to resolve them; say two fighters both stepping away from each other and thus both provoking opportunity attacks. Who swings first then? Reasonably whoever is higher in initiative is the safer fallback. For a grapple on an attack of opportunity, the same concept would apply to an extent where the enemy is moving to exit, but is caught by the back of their clothes and has, as of yet, left their five-foot cube they occupy.

It is a bit confusing but that was how I had seen it handled in Third Edition where this came up more because of all the varied combat maneuvers melee fighters would use. That's all I have to compare it to, but it is not too large a leap, even between editions.

On another note [@Hekazu], would the fleeing men still be in bow range? I imagine so, but I wanted to be certain. I am under the assumption by their next turn they will be outside its effective range for all of us.