This is encounter 1 of a 2 encounter quest.
The encounter ends when all of the vials have been claimed. It's not really important who "wins" this encounter. If the heroes have 2 vials and the overlord has 4, the overlord simply has more.
Why does this encounter matter then? For Encounter 2. Each side keeps the vials that they got in encounter 1. The overlord can use his vials to add surges to monster/lieutenant attacks. The heroes can use their vials to negate surges on monster/lieutenant attacks. Surges are extremely important in Encounter 2 because the Overlord needs them to win the round (His lieutenant needs surges to cause conditions that he can then choose to save up and place in a cauldron. When 4 conditions are in the cauldron, overlord wins)
I think many things in the quest guide is rather blurry. It could be more clear on what to do and not to do.
Like siege of sky tower for example. The guide isnt very clear that only one door at a time can be closed. It only says that levers and door is color coded and that you could either close or open doors.
It can be that english isnt my first language but I'm not that bad at english I think. It also could be a matter of interpretation.