Menachem, there are many things in medrashim that we don’t understand; this is a great example. The rambam rules that if one believes that Hashem gave over command of a part of the world to a malaach, or a kochav, or anything else, he is an oved avodah zara. That’s halacha lemaysoh. Thinking that Hashem gave over fontrol of the world to a tzadik is the same thing.
As to why cunin mentioned Hashem later, i think he betrayed his true belief the first time, which you said is mainstream anyway, but there’s another, even worse possiblity, that he simply uses Hashem and the Lubavitcher rebbe interchangeably r”l.
Tzadikim daven to Hashem and their zchusim protect us; that’s not controversial at all, but it has nothing to do with being under the dominion of a person. Hashem is the only one who has dominion.
What I’d venture to say about the medrash is that tzadikim are a merkava for Hashem, as the tanya explains in perek….2? I don’t remember but it’s in the beginning. They subjugate themselves so much that they are in constant sync with the ratzon Hashem; their ratzon reflects the ratzon Hashem. So it’s Hashem making the decisions but the tzadik acts like a figurehead ruler; it looks like he’s in charge, but really he’s just being gozer what Hashem wants either way.
But that’s not something that “the world will see,” it’s an esoteric concept. When cunin said that the world will see that the Lubavitcher rebbe runs the world, he’s saying it’s a form of giluy Shechina r”l, the kind of thing we daven for by saying vehaya Hashem lemelech etc…we want kovod shomayim to be on full display for the world, that they should all know that Hashem runs the world.
Chabad seems to want the world to know that their rebbe runs the world; goyim should realize that Hashem exists and they should serve Him, not a person. Whatever concepts there are about how tzadikim work in shomayim has no bearing on that at all.