The mask or path that defines the shape scales with the scale of the object. That seems pretty obvious, but if you copy the path from an object with 200% scale to an object with 100% scale, the new path will be half the size of the other one.
If I were doing what you’re doing, I’d create a solid and put an oval mask (I prefer working with solids over shape layers). Put it where I want it in 3d, then duplicate it once (ctrl + d) and move the second one where I want it to be to start it’s orbit, then parent it to a null where the original oval is. I’d duplicate it un-parent the duplicate from the null and rotate the null 90 degrees (easily done by holding shift) create another duplicated, un-parent that duplicate and rotate it again. Repeat this as necessary until I’ve got 4 ovals around the first one exactly the same distance from the center oval and perfectly evenly spaced. You can obviously change the angle to a smaller number to get more ovals. Then link all the ovals to the null and rotate the null.
I hope that helps. Sorry if it’s more information than you needed.