The thing they were searching for was none other than the Divine Dragon Flag.
Even though finding the Divine Dragon Flag in the very beginning won't be that beneficial because the participants won't be collecting that many Darkfire Crystals.
However, these three participants including Twilight were battle breaks and they wanted to fight someone as soon as possible.
Along the way, they killed all the low-level Darfire Wraiths. So, it didn't make much of a difference for them compared to the other participants.
Nevertheless, thanks to their long-range attacking skills, they were able to kill many Darkfire Wraiths and by now, each one of these three participants had already collected more than 100 low-level Darkfire Crystals.
As for the other participants, they collected less than 50 low-level Darkfire Crystals and there were even two participants who collected only 10 low-level Darfire Crystals.