Can Falling Star trigger Immortal Phoenix's ability when it kills a unit, given that Falling Star uses reflexive triggered abilities to deal damage rather than dealing damage directly?

Ruling: Yes, Falling Star can trigger Immortal Phoenix's ability. When Falling Star's reflexive triggered abilities deal lethal damage to a unit, both the spell (Falling Star) and its abilities are considered responsible for killing the unit, meaning the controller killed a unit with a spell.

Sequence:

• Falling Star is played and resolves
• The "do this" phrasing creates reflexive triggered abilities that place two triggered abilities on the chain
• Each triggered ability resolves and deals damage to the chosen unit
• If one of these abilities deals lethal damage, both Falling Star (the spell) and its ability are responsible for the kill
• This satisfies Immortal Phoenix's trigger condition of killing a unit with a spell