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.