When casting Falling Star, when are targets declared, and can an opponent respond to each individual reflexive trigger?

Ruling: Targets for Falling Star are declared when the reflexive triggers are added to the chain (after the spell resolves), not when the spell is cast. An opponent can respond to each individual trigger separately.

Sequence:

• Add Falling Star to the Chain
• Pass priority to opponent (they can cast reaction spells)
• Reflexive trigger occurs - add two instances of 'Deal 3 damage to a unit' onto the chain and choose targets at this point
• Pass priority
• If opponent passes, resolve each trigger one at a time (opponent can react to each trigger individually)