If you're shifting your groups in Z-space (3D) then you sometimes get a parallax effect and it will appear that positioning is "off" when actually the "look at" angle is different. Each group contains it's own 3D "universe" (Local 3D), so another problem might be that your cicles under behavior control are not "centered" when you create them.
For the object that's to have the emitter applied, after you create it, absolutely center it by hitting the Reset control for the Position in the inspector. (You don't have to re-do everything, you can go from group to group and center the original item.) Or, delete all group copies, center the original item, and re-duplicate the group.