Cloning a card with Tribute
Yes, your opponent gets a chance to pay the Tribute. From the Clone rulings:


  Any enters-the-battlefield abilities of the copied creature will trigger when Clone enters the battlefield. Any "as [this creature] enters the battlefield" or "[this creature] enters the battlefield with" abilities of the chosen creature will also work.


This is the same behavior as when you Clone a Triskelion; the Clone will get 3 +1/+1 counters.