Does Immortal Phoenix's ability trigger when a unit is killed by a reflexive triggered ability created by a spell (e.g., Falling Star's 'do this twice' triggers)?

Ruling: Yes, Immortal Phoenix triggers when a reflexive triggered ability from a spell kills a unit. When an ability created by a spell is responsible for a kill action, both the ability AND the spell that created it are considered responsible for the kill.

Sequence:

• A spell with reflexive triggers (like Falling Star) is played
• The reflexive triggered abilities are placed on the chain
• When one of these abilities deals lethal damage to a unit, both the ability and the originating spell are credited with the kill
• Immortal Phoenix sees this as "killing a unit with a spell" and triggers

Nuances:

• This "kill credit" rule is specific to damage/kill effects - it does NOT apply to targeting/choosing effects
• Dreaming Tree (which cares about targeting with spells) would NOT trigger from spell-created abilities choosing something
• The distinction exists because there's a specific rule that tracks kill responsibility through abilities back to their source spell