Does Fallen Star target on cast or on resolution, and can the opponent counter the damage triggers?

Ruling: Fallen Star does not target on cast. After it resolves, it creates reflexive triggers that target, and these triggers enter the chain after Fallen Star resolves.

Sequence:

• Fallen Star is cast and placed on the chain (no targets chosen yet)
• Fallen Star resolves
• Two reflexive triggers are created that target
• Each reflexive trigger enters the chain individually (3 damage each)

Nuances:

• You can counter Fallen Star itself before it resolves (e.g., with Wind Wall), but you won't know the targets yet
• You cannot counter the reflexive triggers themselves
• You can react to the reflexive triggers with other effects like giving units additional might
• The two damage instances are separate and can be reacted to individually, not simultaneous