Who said it was after hours? We don't know exactly what time it is when Squall wakes up in the Infirmary, only that it's morning/early afternoon since the SeeD field exam is scheduled to tae place at 16:00. When Quistis tells him he has yet to complete the Fire Cavern prerequisite before the exam, he mentions (in thoughts) that "[he] was going to this morning, but Seifer..." What I think happened is that as soon as curfew was lifted and he was allowed to leave Garden, Squall decided to go to the Fire Cavern and met Seifer on the way there and they had their duel.