These tests are applied to each position, not to each title or band. Your status is determined by your job duties. For example, Sr. Fiscal Techs, and other grade 8 employees who are now in band 3, are exempt, but others in band 3 are non-exempt. As the new work profiles are rolled out, HR will look more closely at exempt status.
Departments can also call, and request HR to look at the status of particular positions.
The state and university are conservative in applying the tests. By law, any employee who supervises 2 or more other employees can be exempt. UVA may decide that they want to pay overtime to housekeeping supervisors, and the FLSA provides that flexibility. The FLSA was written in 1938 for a manufacturing environment. It doesn't really fit higher education that well.