Thank you Lexi_Summers for the answer, sorry I use a translator, it can create misunderstandings.
No, the model does not stop the stream and does not put it in spy mode on another site, the show is visible on the other site.
An example, on SC I go with a model in a private show (exclusive or not, it doesn't matter), on CB my show is visible to everyone. What's the point of requesting a private show if it isn't?
And it's like that in the reverse direction CB to SC.