Timelines won’t sync across different layouts. Layouts themselves can be thought as independent scenes with their own elements and timelines.
If you want content such as Timelines to be synced across different layouts, you can use Symbols. Symbols encapsulate their own elements and timelines. The thinking is that if you can’t put it in a symbol because it is different between layouts, then you probably wouldn’t be able to sync the timelines either! The other option is to copy and paste animations from the timeline.