@Miku39: It’s not like anyone knows how many Stille there are in the area. There may be enough for everyone, and there may not. Beyond that, though, the mages may not necessarily have the ability or thinking power to catch a Stille, but could have an easier time snatching a caged Stille from another examinee. There isn’t really a hard set of qualities they’re looking for in this exam, just that the applicants are able to achieve the goal with the abilities they have.
I assume that rule about the barrier may be for those who have the ability to leave the barrier. You’re not disqualified for leaving, after all, only for not being inside when time is up. Guess the examiners are willing to consider this kind of rule skirting stuff.