Should I be working off the clock?

I’m a full time Site Supervisor, paid hourly, NOT salary, scheduled and work 40 hours per week, zero benefits at this site, and no overtime period. My dilemma is that the client and the account manager expect me to be available to work 24/7 outside of my regular shift without additional pay. Just this past week, the client calls me up and before I can even say “how can I help you” they tear into me about apparently not answering my phone for the overnight shift supervisor so that shift supervisor called the client at 2:00 AM. They kept ranting and raving, not even giving me a chance to tell them that my phone never rang and the call log proves that. After a full minute of their ranting and threatening to get the branch manager involved, I simply reminded them that I am paid hourly, not salary, and AUS policy states that any work done outside of my scheduled hours must be approved in advance. I added that I had already worked a considerable amount of time outside of my scheduled hours, and I would be happy to present that to the branch manager should they choose to get them involved. The client hung up on me and called my AM. My AM texts me stating that the whole reason I get paid more is because I’m expected to work off duty. (FYI - I make $2 less per hour than the average site supervisors in my region, but possess the skills and experience to qualify as AM and above). For the record, I have always answered my work phone off duty and helped out no matter what (unless I’m literally unable to while showering or using the restroom) and helped in any way that I can. Because I know what it’s like to be the person reaching out and needing help but no one answered the phone. But the majority of the time it’s an issue I can’t assist with (like scheduling or payroll because AUS still hasn’t given me access to the resources needed). But I do still immediately pass along the info to someone that can assist. Am I crazy for thinking this is just wrong for them to demand that I work off the clock without pay, even though I’ve always been available (but on my own accord and not due to a demand)? People outside my work environment are telling me to just put up with it and go with the flow until changes happen, but that just doesn’t sit right with me. If I was salary, I’d understand. Or even able to put in an adjustment for my time spent working off site. But no, I’m literally expected to be available to work anytime anyone needs me when I’m off the clock, with no additional pay. And even get yelled at by the client when they incorrectly assume that I didn’t answer my phone ONCE. Please tell me I’m not in the wrong here with my feelings. The other sites I’ve worked did not operate this way, and I’m left speechless at how horrible everything else is going. I have reached out to two other AMs that I used to work with and both have told me to absolutely not work off the clock without submitting my time. But even if I did submit my time, it would not be approved (over 11 hours I’m owed if I were to do that, and that’s just for the past couple of weeks).

What the heck should I do here? Go ahead and request a transfer to another site (which the AMs I reached out to already said they’d find me options), or keep dealing with this because it’s apparently the new expected norm?

I have never in my life dealt with such insane levels of bullshit until this site (and I’m pretty friggin old and seen a lot of bullshit).

Rant over, but please give me honest advice and tell me if I’m the problem or just this site.