Dear Gods, YES, I wish the daily league quest was set to start at the same time every day! Finally figured out what causes the fluctuation, as I was puzzled by it for quite a while. The new league quest is only activated when any league member logs into the game after the previous league quest has finished, not automatically, nor will it register while logged in until you refresh. So, leagues that are very active with many members won't see huge differences in when it begins, although it'll keep edging later and later.