Well I've spent the last 5 hours trying to replicate the issue. But so far have had no success. The original project where the issue was present was ok after setting each of the affected objects to single user.
All I can do is post a .blend file if I come across the issue again.

I do not have the original blend file but will create one that exhibits the condition.

Please refer to blender manual under datablocks. It describes the links that remain.

Unfortunately i corrected the issue and it has gone. Along with the failing blend filen as after correction it was over written. But i will locate the page in the blender manual that describes these "soft links". If i recall material settings and f-curves remain linked between duplicated objects.

Think i may have found the problem after doing a bit if digging around and googling. It seems to be related to duplication, and the "soft links" that remain between the duplicates. So selected each sphere in turn . And in its' IDdata set it to make single user.
I have now been able to succesfully setup my node tree on one sphere. And it appears to work correctly when i adjust the strength of the Emission Shader.
The "soft links" for duplicate, can be set somewhere in preferences. So I'll now set them up in prefs.