At my former carrier, a reserve was under no obligation to be contactable on a day off. Thus, on your first day of a long call reserve shift, the earliest you could be given an assignment was noon. (I.e., contacted at midnight for a noon report.)
My understanding of the UAL policy is that even on a day off, you can still be assigned something for the following day of long call reserve. For example, if I am off today and begin long call tomorrow at the stroke of midnight, they can still call me today for say a 9am flight or short call conversion, and this is considered a legitimate assignment. Do I have that right?