Nice job grieving it. That must mean your steward is behind you. Hopefully all this will be fixed.
I REALLY don't like that sit beside the phone for an hour part. By having you sit there, your management team is covering their own ineptitude. Any management team should know what's covered or not well before the start time.
Over is right. This is what I think is reasonable: call 1 hour before start time. If they need you, come in, if they don't or they don't know by then, I think you should be able to make other plans.
Seriously, how can your center team not have their bases covered 1 hour before start time? If you can work on the side when not working at UPS this should give you even more incentive to not agree to their demand of "an hour after start time"?
Just let your steward or BA know whats going on and they will have it iced immediately. I say this because if you are a full-time senority employee then you have rights. Those rights include that you don't have to "sit by the phone for an hour". They also include that if you show up for work you are allowed 8 hours of work.
Don't let them push you around, because they will, and they will push and use new-hires because you don't know the rules of the contract. I can't blame management because it is smart business on their part. Its up to you to know the contract. Look for union support and life will be better for you.