If the Organization of Water were compared to a person, then this person's hand now holds a very sharp knife.
Why does someone else joining the Organization of Water become part of it, while Cerberus joining only makes them a knife? The reason is simple. Yang Yi may never be able to truly consider these people his own, so they can only be a sharp knife, one that can be held but not part of the body.
Settling Karl Stemonsen was easier than anticipated, but that's normal, because these people from Cerberus were already at their wits' end; otherwise, they wouldn't have ended up being taken in by Gong Yang. Since they are desperate, and Gong Yang can't keep providing shelter for them, what choice do they have but to follow Yang Yi?