There's no incentive for the lunarians to betray Phos, so Cairngorm action must be within the scope of rescuing.
Furthermore, they didn't take the other shattered gems. So in this case, Lunarians fully respect Phos plans.
In other side, Adamie's disappearance may be related with pacifist euclase's plans which seek the best ending where all gems will unite for once again. Because if he enter the fray before Bortz vs Phos and Pad vs Quack battles, all will be resolved without those gems understanding each other