끝나다 is intransitive — a thing ends by itself — and the -아서/어서 clause gives what preceded the ending. Half of these lines use the fuller -고 나서 끝나다 ('end after having done X'), as in 집중하고 나서 끝났을 때의. Elsewhere it marks a time passed (10시 넘어서 끝났어, it ended after ten) or pairs with the start ('우와'로 시작해서 끝났을 텐데, it would have begun and ended in awe).