Using a single task list, from our testing it seems that the add to timeline/remove from timeline functions store state across the site list rather than against the view.
Is it possible to select a view and display different timeline state?
Edit:
By state I mean that there is that property information for the list (i.e. which tasks should be shown seems to be a list property).
Ideally we wanted tasks shown in an instance of a timeline control to be able to be customised/filtered per instance or determined via a list view.