I think I recall talk of multiple 360 rooms so I would assume they would split the cars to enter different theaters.
It's not exactly that.
I would suspect both are in the same 360 room, but what comes before will be something that is highly fascinating.
This was a cause for issues in Hollywood, and I suspect its becoming issue now for Orlando, but in the musion room for Hollywood, all of the Tram cars (four, btw) that all have separate rooms. They don't all share one room, think like the original Journey to Imagination.
But that what Hollywood had problems with, was that the tram cars being used were having issues with sensors, due to the second, third, and fourth tram cars all having their front view blocked off by rolling doors, that blocked viewing of the scene from in-front of the others point of view.
It's a fascinating mechanic, and something that is very much unique in many ways. And that they have gotten the problems fixed when I was there back in 2016, before Hogsmeades opening.
If I had to guess what the seven blazes is going on, to be blunt, Universal Creative is dealing with nearly the exact same problem to what Hollywood had with that musion scene originally of the doors, and that they are trying to troubleshoot it as fast and efficient as possible to get the best outcome.
EDIT: To give a rough mock-version: