Yes. Check in the properties dialog of the slideshow. The first parameter defines the behaviour of the slideshow during scene switches (pause, continued play, restart...)
I hope you hadn't copied the slideshow between scenes at all! From the second scene on you should have used "Adding existing:..." at time of insert the slideshow. IF not, you'll have three independent copies of your slideshow, what isn't at your will.
When I switch between themes with the same slideshow (yes using "Add Existing") it still restarts itself no matter what that setting is. This doesn't seem to happen unless Studio Mode is enabled, so maybe it's a bug with Studio Mode.