The cutoff at the end of the round is there to prevent characters from being able to take 2 turns in quick succession, which can allow them powerful effects like being able to apply a bane (such as Incapacitated) to the enemy and then immediately attack them while they’re weakened. You can consider it that due to the poor initiative roll your reactions in this fight are too slow to be able to interrupt anyone above you in the turn order.
However, I do allow players to hold their actions for trigger in between rounds as long as it’s clear they’re not abusing the system. As long as they have a legitimate reason to wait, such as the enemy being out of range, it’s mostly fine. If it gets back around to the player’s turn and the trigger has not occurred, their held action is lost. Please note that this is a house rule, the way I explained it in the first paragraph is how the rules actually work for this situation.