The problem is the one I mentioned before: because of how the viewports are updated and the fact that the scene is taken out of one side and inserted into another, animations like the one you show end up becoming desynchronized by a few frames. You have to control that manually in your scripts.
I’ve added two signals to the pageflip script. You can download the new file and play with those signals to “synchronize your scenes.” The signals are started_page_flip_animation and ended_page_flip_animation, and they are emitted when the page-flip animation is about to start and when it finishes.
To connect those signals to your scripts, you can use the BookAPI so your scenes can retrieve the active book when they enter the scene tree (var book: PageFlip = BookAPI.get_current_book()). From there, you can connect to the book’s signals to synchronize your scenes.
You can do this when the scenes enter the tree: get the book, check that you’re not already connected to it, and then connect it to your script. The logic to actually synchronize the pages is something you’ll need to implement yourself.
By the way, in the pageflip inspector, if you enable enable_composite_pages and assign a page texture (the blank sheet of paper) to blank_page_texture, textures/scenes with transparency will be drawn on top of the paper.