IANAL, but isn't this outside the court's scope of authority, as many (most?) aren't parties to the case? As I understand the role of judicial review and precedent, I don't see how a party not associated with a case can be compelled to do anything without a due process opportunity.
I'm pretty sure they will do what their lawyers tell them the judge had the authority to do. If the judge does not have this authority, their lawyers will tell them to ignore it. If they judge does, they will tell them to obey it.