My opponent activated Magician's Circle. I countered it with Twister. The effect of M. Circle went through even though it was destroyed before it could resolve.
Is that right? Or is that a bug? It definitely seems like the effect should have been cancelled.
No it's not a bug. The effect will continue. Destroying a card does not equal to negating it's effect, unless you are talking about Continuous Spells/Traps.
Twister can only destroy cards. It can't negate activation. The only time it'll work as a counter to a spell/trap card is if it has an effect that requires the card to stay on the field, like mirror wall or a field spell.