No they see my screen, and a small picture of themselves. Then even when I close the small window of them, so I can't see it, they still can. Even when I set up two screens and shared only the one with the slides on, and have the Skype window open in the other, non-shared screen, they can still see themselves.
Them on laptop not phone makes a difference, then they can turn off the small window with them in. No way to get a little window of me it seems, but less critical.
No they see my screen, and a small picture of themselves. Then even when I close the small window of them, so I can't see it, they still can. Even when I set up two screens and shared only the one with the slides on, and have the Skype window open in the other, non-shared screen, they can still see themselves.