Hi,
I'm not aware of that functionality in Zephyr Scale. It works with the Jira Issues but I've not seen it work with the assignment of test cases. You Depending how many testers you have, you could setup a report for each that list all their test cases. To do that:
Go to Reports
Choose Test Execution folder
Choose Test execution results (list) report
Filter by: Custom Query
Test case: add condition = Owner In [add your tester here]
When you execute the report it will list all test cases for that tester. You can then share the URL of the report with that user. The URL is dynamic and will update. There are many more options available in the Custom Query to help you build good reports. For example, to exclude test cases that have been executed and have a result of Pass, you would add a condition into 'Test execution' and select Result Not In Pass.
Hope that helps.