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.