Are you FLSA exempt? If you are not, and your supervisor is expecting you to answer messages for work related stuff off hours, it is likely an FLSA violation (unless they are paying you overtime). If exempt, then you'd have to look at your organization's employee relations manual for how they handle off-hours contact from your supervisor. I think I remember you were PharmD? So likely exempt, per federal regs but wasn't 100%.
As a supervisor myself, I am always wary of any potential FLSA implications for anything I do/ask of my people. I will not ask for, or allow off-hours work, as much as I'd appreciate it. If I am aware and allow it, I am responsible for it.
As far as I am concerned, when you are off, you are off. If they need to have contact with you on off hours, setup an on-call policy and appropriate compensation with it. Either a per-diem, or per-event basis, or build into base pay if everyone agrees to it ahead of time. But, don't ask for more off hours contact for free.