When does Blue Teemo pick targets for his effect and when does he need to pay Deflect costs?

Ruling: Teemo chooses a single target when his ability enters the chain (when Deflect costs must be paid), then reveals Hidden cards to determine how much damage that target takes.

Sequence:

• Teemo's ability enters the chain
• Teemo chooses one target and pays any Deflect costs
• Hidden cards are revealed
• Damage equal to the number of Hidden cards revealed is dealt to that target

Nuances:

• Teemo does not ping multiple times like Icathian Rain; he deals all damage to one target
• The interaction with Void-Gate effects was initially answered incorrectly in this thread and was later corrected in a separate discussion