If you refresh a page you are firing many requests. Most likely, some of those requests are executing the qa-blob.php or qa-image.php files (for example, because of the use of avatars). So you are bootstrapping Q2A several times on a "page refresh".
Whether this makes sense to you or not, depends on your requirements. If you want to only execute that code once maybe it might be better for you to add it to a layer. For example:
public function initialize() {
parent::initialize();
$qa_count_user_visits = isset($_COOKIE['qa_count_user_visits']) ? (int)$_COOKIE['qa_count_user_visits'] + 1 : 1;
setcookie('qa_count_user_visits', $qa_count_user_visits, time() + 86400 * 365, '/', QA_COOKIE_DOMAIN, (bool)ini_get('session.cookie_secure'), true);
}