It is not uncommon to have a couple of drivers "on call" on these non-operational days. Drivers asked to be "on call" generally have to call by a certain time to see if they are needed or not. No, the time spent being "on call" is not paid time. They put drivers "on call" in case they receive unexpected volume or if a driver already scheduled to work calls in. Generally drivers "on call" end up not having to work---they are simply a safety net in case something goes wrong.
To those who suggested the OP simply turn off or not answer his phone---it is easy to give this advice when you are not the one who will have to deal with his mgt team on Monday. While they cannot discipline him for not being available while "on call" they can certainly give him some grief over blowing them off.
The alternative would be to over-staff and then send people home.
Does any driver at UPS really care what management thinks of them? All my driver sups are fat, lazy and incompetent, not to mention their gone by 430 everyday. No Full Time employee (except feeders) should be placed ON CALL, its not in the contract. Management likes to make up new policies as they go. If we alllow them to do this our contract is meaningless.