3 Employees (2 Non-Exempt, 1 Exempt) are required to carry an on-call cell phone on a rotating basis, ie; every 3rd week)
During that time we must be within 30 minutes of our work site in case our presence is needed.
We only get compensated for time actually spent at the center. No compensation received for the actual "on-call" time even though it interveres with our personal time.
What do you mean by non-exempt and exempt employees?
Regardless, absent a written contract for employment (or labor agreement if you are in a union, which you likely aren't since this is a non-profit) saying otherwise, yes, an employer can do this legally in Ohio.
The policy is a requirement for your continued employment there. I don't know what your non-profit does that requires someone to be on-call, but it's unreasonable to expect an employer to pay you simply because you're "on-call" until you're called in.