As Kaito Shizuki phases out, Auras attached to him also phase out at the same time. Those Auras will phase in at the same time Kaito does, and they'll phase in still attached to Kaito.

Permanents phase back in during their controller's untap step, immediately before that player untaps their permanents. Kaito phases back in with the same number of loyalty counters that he phased out with.

Phased out permanents are treated as though they don't exist. They can't be the target of spells or abilities, their static abilities have no effect on the game, their triggered abilities can't trigger, they can't attack or block, and so on.

Phasing out doesn't cause permanents to leave or re-enter the battlefield, so no "leaves the battlefield" or "enters the battlefield" abilities will trigger, and Kaito's first ability won't trigger again at the end of a turn in which he phased in.