Warped cards still return to exile despite being phased out

[Edasiba]

As far as I know, when a card is phased out "at the end of the turn" effects should no longer affect it. I played [[Starwinder]] warped in and in the second main phase, played [[Talon Gates of Madara]] targeting it to be phased out. Despite this, the Starwinder warp trigger still went on the stack and returned the Starwinder to Exile.

[github-actions]

Starwinder - (Gatherer) (Scryfall) (EDHREC)

{5}{U}{U}
Creature — Leviathan
7/7
Whenever a creature you control deals combat damage to a player, you may draw that many cards.
Warp {2}{U}{U} (You may cast this card from your hand for its warp cost. Exile this creature at the beginning of the next end step, then you may cast it from exile on a later turn.)

Talon Gates of Madara - (Gatherer) (Scryfall) (EDHREC)

Land — Gate
When this land enters, up to one target creature phases out.
{T}: Add {C}.
{1}, {T}: Add one mana of any color.
{4}: Put this card from your hand onto the battlefield.