After Quenchable Fire resolves, the targeted player becomes able to perform a special action of paying {U}. This action may be performed any time the player has priority, and it doesn’t use the stack. It may be performed only once, and only before your next upkeep begins. If the player has performed the action by then, the “deal an additional 3 damage” ability won’t trigger. Otherwise, it will. If it triggers, the player can’t stop it by paying {U}.

Quenchable Fire’s delayed triggered ability (and the special action of paying {U}) will affect the player who was targeted by the spell, even if the original 3 damage is prevented or redirected to a different permanent or player.