Do Icathian Rain and Falling Star trigger Immortal Phoenix when they kill it with their reflexive damage triggers?

Ruling: Yes, Icathian Rain and Falling Star trigger Immortal Phoenix. When a spell creates a reflexive trigger that deals damage and kills a unit, both the ability and the spell that created it are attributed with the kill action.

Nuances:

• Initially, the rules defined "killing" a unit with a spell as dealing damage during the spell's resolution, which would exclude reflexive triggers that deal damage after resolution
• The rules were updated to clarify that abilities generated by spells that cause kill actions are attributed to both the ability and the game object that created them
• This attribution applies specifically to deal and kill actions, not to other spell properties like targeting (e.g., Dreaming Tree still does not work with these spells' reflexive triggers)