Without seeing exactly how the data is structured and how the view is set up, it's difficult to give an exact answer. I used the provided sample data to create a table join between the Product_Sales table and the User_Access table. While I don't have those users on my Tableau Server I was able to test the behavior by creating a view with manager from User_Access and product from Product_Sales:
This appears to be the desired behavior. The issue may be with how the table join has been created. Below I have a screenshot of my table join:
If you are able to share a packaged workbook that demonstrates the experienced issue, then I may be able to give you more specific advice. Check out Anonymize your Tableau Package Data for Sharing for instructions on one method of anonymizing data so it can be shared.
This should work perfectly. We use this all the time.
However , the issues we face is
a. The names in the Tables do not exactly match the Tableau Usernames
b. If they match they are not of the same case.
c. We use the userfilter as upper(username()) = upper(Manager) instead of fullname() = Manager
d. Duplicating of Data (if the userfilter is not set)