Does Falling Star's ability trigger Dreaming Tree's draw effect when targeting your own unit?

Ruling: No, Falling Star does not trigger Dreaming Tree's draw effect when targeting your own units.

Sequence:

• Falling Star creates 2 reflexive triggers that each deal 3 damage
• These reflexive triggers are put on the chain
• The triggers deal damage but are not themselves spells
• Dreaming Tree only triggers when a spell targets your unit, not when a reflexive trigger does

Nuances:

• The reflexive triggers count as spell damage (a special case that only exists for damage)
• This makes Falling Star and Itachian Rain behave differently from regular damage spells in multiple situations
• Regular damage spells would trigger Dreaming Tree, but Falling Star does not