Tributing 1 monster is a cost.
You must use "Summoner of Illusions"’ effect when it is flipped face-up, either by Flip Summon or by being attacked. If you have no cards in your Fusion Deck, the effect cannot activate and you do not Tribute 1 monster.
If you use "Dimensionhole" on the Fusion Monster summoned by this card’s effect, it will return during your next Standby Phase and not be destroyed.
If the Fusion Monster summoned by this card’s effect is flipped face-down it will not be destroyed during your End Phase, since the condition is reset when the monster becomes face-down.