We allow you to "target" those questionnaires in various ways; e.g. you can choose to display the survey only to people who have spent atleast 60 seconds on the page. Take a look - http://webengage.com/survey#targeting
Plus, you can always choose to use the feedback tab which is passive (only opens when the user clicks on it) and not proactive like surveys.
If all of the above didn't make any sense, we have a JS API to open the survey at the click of a link at the bottom of your page :-) - http://docs.webengage.com/api/js-api.html#survey-api