The exiled cards return to the battlefield immediately after Hixus leaves the battlefield. Nothing happens between the two events, including state-based actions.

If Hixus leaves the battlefield before its triggered ability resolves, the creature that dealt combat damage to you won't be exiled.

If a creature token is exiled, it ceases to exist. It won't be returned to the battlefield.

In a multiplayer game, if Hixus's owner leaves the game, the exiled cards will return to the battlefield. Because the one-shot effect that returns the cards isn't an ability that goes on the stack, it won't cease to exist along with the leaving player's spells and abilities on the stack.

Hixus's ability causes a zone change with a duration, a style of ability that's somewhat reminiscent of older cards like Oblivion Ring. However, unlike Oblivion Ring, cards like Hixus have a single ability that creates two one-shot effects: one that exiles the creature when the ability resolves, and another that returns the exiled card to the battlefield immediately after Hixus leaves the battlefield.

Auras attached to the exiled creatures will be put into their owners' graveyards. Equipment attached to the exiled creatures will become unattached and remain on the battlefield. Any counters on the exiled creatures will cease to exist.