Do you think logout urls could be updated to use wp_logout_url( $redirect ) instead of the hardcoded links you use now. The current behavior means a user is presented with an intermediate page confirming the logout.
An example change would be in class_wdfb_marker_replacer.php on line 44.
If it could be changed from:
$logout = site_url('wp-login.php?action=logout&redirect_to=' . rawurlencode(home_url()));
$logout = wp_logout_url(home_url());
That should prevent this behavior…