MTG HELP! tap in response to a tap?

ok my friend uses captain sisay. you tap the captain to search your library for a legendary and put it in your hand. can i use icy manipulator (1tap: tap target creature or artifact) to tap the captain *in response* to my friend tapping her to use her ability? wouldnt my tapping her *in response* cause her to tap before he tapped her to use this ability?