Volunteers are exempted from minimum wage requirements. But there is nothing in this job posting indicating that this is for a volunteer position.
This position is unpaid at a public not private employer. In this case the commonly understood meaning of "volunteer" is likely the same as the legal one.
If you pay someone more than $0, that’s when you need to pay them at least minimum wage.
> FLSA prohibits public sector employees from volunteering, without compensation, to work additional time performing the same type of services or work for which they are employed. For example, a police officer can properly be considered a volunteer, and need not be paid, for reading to school children at the municipal library. The same officer must be paid, however, and cannot be considered a volunteer, when directing traffic for a city-sponsored road race in the same municipality where the police officer is employed.
So I guess if you already have a position in another state school, you apparently can't take this one.
[1] https://www.wardandsmith.com/articles/wage-hour-law-voluntee...
The "without salary basis" looks pretty clear to me, and I'm sure someone holding a PhD could spot that as well.