If you Tribute Summon “Thestalos the Firestorm Monarch” successfully, and your opponent discards a monster like “Oustanding Dog Marron” or “Regenerating Mummy”, you still inflict damage because the monster was discarded to the Graveyard (even though it doesn’t remain there).
If “Banisher of the Light” is face-up on the field, no damage is inflicted because the card is not discarded to the Graveyard.
This card's effect always activates when Tribute Summoned, even if your opponent has no cards in their hand.