Record type assignments were never intended to work in situations where there are multiple records (Like on a tab page). Page assignments is looking for a single record in this case, and based on its record type it is sending you to a particular page.
If you are trying to show the particular user only one record type - use conditions, not page assignments.
Are you trying to show different contents in the tabs for different profiles/users? If so you can use the other type and type the name of your tab and then Pick “tab” type from the drop down and that will change the page per profile/user while only consuming one salesforce tab. But if you just want record type different data to show up then you have to use conditions or different models/pages. Maybe clone the page for the different scenarios and do the tab based assignments.
If record type assignments were not intended to be used with tabs, why is that scenario used in this tutorial example?
And in the linked example, is there a benefit to using page assignments when creating a Visualforce tab?