I see (or hear) what you're talking about -- if you use the voice search within the YouTube app and speak the search term, the app will speak back the search term after showing the results.  Not sure if there's a way to do that, because this seems to be a specific search function for YouTube only, rather than a universal Google search.  Let me dig a little deeper.
EDIT:  Nope, couldn't find an option to turn it off.  You can send feedback to YouTube about this.