This card can be activated even if your opponent does not control any monsters. This effect is not only applied to monsters your opponent controls when the effect resolves. During the turn this card is activated, if your opponent Special Summons a monster, that monster can be Tributed for a Tribute Summon.
When this card resolves, a Tribute Summon is not performed. Once during the turn this card was activated, if you would Tribute Summon a monster, you can Tribute 1 monster your opponent controls. Therefore, even if a monster your opponent controls is Tributed for a Tribute Summon, that monster is not treated as being sent to the Graveyard by a card effect.