Shady Traveler // Stalking Predator

If it is day, and the active player of the previous turn cast no spells during their turn, it becomes night.

If it's neither day nor night, and a creature with daybound and a creature with nightbound somehow appear on the battlefield at the same time, it becomes day. The creature with nightbound will transform.

Before a player untaps their permanents during the untap step, the game checks to see if the day/night designation should change.

Permanents with daybound and nightbound can't transform via any means other than their daybound and nightbound abilities. Notably, older cards such as Moonmist that instruct a player to transform permanents don't affect permanents with daybound or nightbound.

Double-faced permanents with daybound transform to their nightbound faces as it becomes night. Similarly, double-faced permanents with nightbound transform to their daybound faces as it becomes day. This happens immediately and is not a state-based action. It happens any time it becomes day or night, not just during the untap step.