It sounds like your problem is caused by the location of the object origin.
Procedural textures often use the object origin as the location or reference point for the procedural texture.
You could try selecting the eye first then the eye disc, so the disc is the active object, then CTRL+J to join.
This should keep your eye disc texture correct, but will probably mess up any procedural texture on the eye part.
Another option is to adjust the texture mapping node in the procedural texture, but this will be a trial and error operation until you get it right. WARNING: Possibly cause major frustration.
If you can share the .blend file, we could take a closer look and find a solution.
But I do wonder why you made the choice to use separate objects, only to join them anyway.
