Here’s what I would do:
* Make the random effector a child of the plane and then zero out the effector’s rotation;
* In the effector’s parameters tab, set the transform space to effector.
Now the sphere’s will rotate with the plane. Of course you have the random effector set to use global turbulence, so when you rotate the balls will slide around. If you don’t want that, set the turbulence to use UV space.