MTG: Responding to Activated Abilities.?

I have a Lin Sivvi in play. I tap four mana, tap Lin Sivvi, and announce I am searching my library for a Rebel with converted mana cost four or less. My opponent says, in response, I cast unsummon on Lin Sivvi. Lin Sivvi goes back to my hand. Am I correct in uming that I still get to search for a rebel since it was placed on the stack and Unsummon was cast in response to her ability?