Unfortunately your objects in one instance of Invigorator are not related to the objects of another instance of Invigorator. So, if you decide to apply a material to one instance, you will have to go in and apply them to the objects in the other instances as well.
If you are working within one Composition, you shouldn't need more than one instance of Invigorator unless you are animating more than 8 sets. If you are working with less than 8 sets, you can consider placing the objects all within one instance of Invigorator. Then, it would be easier to apply the materials on your objects.