The second ability of Neyali, Suns' Vanguard triggers for each player you are attacking with one or more tokens. It does not trigger if you are attacking a planeswalker a player controls, but not that player.

The card Neyali exiles is exiled face up.

The effect allowing you to cast the exiled card if you attacked with a token continues to apply even if Neyali leaves the battlefield or another player gains control of it. It also continues to apply during later turns—as long as you attacked with a token during those later turns.

You can cast the exiled card if the token that attacked is still in combat, if it's left combat, if it's left the battlefield, or even if combat is over.

Neyali's effect doesn't change when you can cast the exiled card. For example, if you exile a sorcery card, you can cast it only during your main phase when the stack is empty.

Casting an exiled card causes it to leave exile. You can't cast it multiple times.