The game is synced to your device's date and time. This means that 1 in-game day is equal to 1 day in real life.

Campaign days always start and refresh at 5:00 AM local time. This is important to note because if you completed all of the quests for a day, you're going to need to wait for the next day to start to receive new quests and progress the story.

Meanwhile, some of the mechanics influenced by your device's time include the day/night cycle and timed quests. For the latter, timed quests will use your device's time to track how much time is remaining before it expires.

Note that timed quests are entirely optional and not story related. They won't affect your relationship with a bear or your overall progress in the game. They also repeat, so don't worry if you can't complete one as you will get another chance eventually.