The fight between Venessa and her Frozen Sun opponent ended a lot sooner than was expected. However, it can be mostly attributed to the excellent strategic lineup of the Frozen Sun staff, they knew which of their students would have the most advantageous time against her, and chose to have him go first.
Moreover, since only 3 contracts at a time could be summoned in Phase One, Dark Moon hadn't known that this particular participant would be so difficult for Venessa to handle since this ice golem and another powerful contract weren't revealed in Phase One, nor did he participate in any of the earlier Phase Two matches.
Did they intentionally not reveal much of their strength in Phase One to bank on a higher ranking in Phase Two?
If so, Kain had to admire their guts. If anything went wrong and Frozen Sun had a lackluster performance in both phases, they may be the subject of unfavorable public scrutiny.