At the very moment the man that barred them from heading into the dungeons in the first place finally gave them the green light to move forward, a few of the people in the group made a mad dash towards the dungeons they've chosen, their bodies disappearing before they could make contact with the respective entrances.
As for Valyr and the others, they took a more relaxed approach to getting to the entrances, considering that each and every of them would separate after they entered their dungeons. To those that only had the strength at the peak of Rank 1, they surprisingly heeded the words of the man from earlier and decided to not take too much of a risk, entering the Common Caves to the very left.