You must destroy 1 Spell or Trap Card on your opponent’s side of the field to be able to Set 1 Spell or Trap Card. If your opponent chains a card to destroy the target of “Dust Tornado”, you cannot then Set a Spell or Trap Card because “Dust Tornado” did not destroy a Spell or Trap Card. If your opponent activates the card targeted by “Dust Tornado” it is not negated, but is still destroyed by “Dust Tornado” so you may Set 1 Spell or Trap Card.
Netrep Rulings:
A non Quick-play Spell Card set by the effect of “Dust Tornado” during that player’s Turn may be activated during that player’s Main Phase 1 or Main Phase 2.
If “Dust Tornado” is chained to “Harpies’ Feather Duster” or “Heavy Storm,” and “Dust Tornado’s” second effect of Setting a Spell or Trap Card is used, that Spell or Trap card will be subject to the effect of “Harpie’s Feather Duster” or “Heavy Storm.”