If the local admin is assigend as key contact to an employee, of course, they will see the tasks assigned to themselves.
If the admin has the same filters as the employee and has access to the tasks library, they will see the tasks related to this employee in the task library.
Otherwise, if the local admin has access to the task library but not the same filters as the employee, they won't see the tasks linked with that employee, as their filters don't match.
If you still have questions after reading this article, don't hesitate to contact us by submitting a ticket.
We're always happy to help ! :)