You're right, its not different than fates. As a Paladin you can flash spam everything in a fate, as a Black Mage you can scathe everything in a fate. And then let everyone else kill it and get full credit.
Aka, the first group that pulls gets full credit... Guaranteed. Everyone else have to compete with each other. If 'everyone else' hits the mob once for a few damage and there is enough people there that that 'few damage' each is enough to add up to kill the mob (as it was in my experience above) then credit goes a little 'wonky'. As in many people won't get credit and many will get little credit. But the first group that pulled the mob, will get full credit, regardless of the damage they did.
Hence.... you see the mob, get your group there and pull it as soon as possible. That's how it was designed. If its not how it was intended (design can be different from intent). Then they'll change it. But until then, grab it and kill it before it goes up to lady luck to decide who gets credit.