If you have given the supervisor employee "Supervisor" permissions in the permission page by using the preset, then it should be fine, they can just press the "Add: Absence" button (upper right) on the MyTimeSheet page. If they don't see that button, then they don't have proper permissions.
when I set the permission to "Supervisor(All Employees)" it works fine. When I then set it to "Supervisor(Subordinates only)" I get the permission denied error.