That's how story works. Tableau saves parameters/filters settings within each story card (also called story point). That enables you to have same dashboard with different settings saved in different cards in one story. Story is not designed to be used as a presentation tool, what I see pretty often. In my opinion that is bad practice.
I would advise using standard Tableau tabs.
Global filter will not work one Story tab to another.
Go with dashboards and use global filters.