"exile until ~ leaves the battlefield" triggers too late

[Thelk641]

-- The situation

[[Rampaging Baloths]] exiled under [[Glorious Protector]]. I cast [[The Great Aurora]].

-- What happens

The Aurora resolves completely, then xmages shows a Glorious Protector trigger, puts the Baloths on the battlefield, then everything else resolves : the Baloths arrives after the Aurora has put lands on the battlefield.

-- What should happen

The cards exiled with Protector should come back as soon as it leaves, even if it's mid-resolution : the Baloths should be on the battlefield when the Aurora puts lands there, which means it should see them and trigger.

[github-actions]

Rampaging Baloths - (Gatherer) (Scryfall) (EDHREC)

{4}{G}{G}
Creature — Beast
6/6
Trample
Landfall — Whenever a land you control enters, you may create a 4/4 green Beast creature token.

Glorious Protector - (Gatherer) (Scryfall) (EDHREC)

{2}{W}{W}
Creature — Angel Cleric
3/4
Flash
Flying
When Glorious Protector enters, you may exile any number of non-Angel creatures you control until Glorious Protector leaves the battlefield.
Foretell {2}{W}

The Great Aurora - (Gatherer) (Scryfall) (EDHREC)

{6}{G}{G}{G}
Sorcery
Each player shuffles all cards from their hand and all permanents they own into their library, then draws that many cards. Each player may put any number of land cards from their hand onto the battlefield. Exile The Great Aurora.

[HexOoze]

-- The similar situation
[[Notion Thief]] phased out with [[Out of Time]]. I cast [[Sway of the Stars]].

-- What happens
The Notion Thief reappear after the whole Sway of the Stars resolves.

-- What should happen
The cards phased out with Out of Time should phase in as soon as OoT leaves, even if it's mid-resolution; the Thief should be on the battlefield before the SotS let players draw cards, which means it would replace that event.

[github-actions]

Notion Thief - (Gatherer) (Scryfall) (EDHREC)

{2}{U}{B}
Creature — Human Rogue
3/1
Flash
If an opponent would draw a card except the first one they draw in each of their draw steps, instead that player skips that draw and you draw a card.

Out of Time - (Gatherer) (Scryfall) (EDHREC)

{1}{W}{W}
Enchantment
When this enchantment enters, untap all creatures, then those creatures phase out until this enchantment leaves the battlefield. Put a time counter on this enchantment for each creature that phased out this way.
Vanishing (At the beginning of your upkeep, remove a time counter from this enchantment. When the last is removed, sacrifice it.)

Sway of the Stars - (Gatherer) (Scryfall) (EDHREC)

{8}{U}{U}
Sorcery
Each player shuffles their hand, graveyard, and all permanents they own into their library, then draws seven cards. Each player's life total becomes 7.