Actually you shouldn't see "do you want to logout" when logging out from Sphinx using the Logout method. Are you using it?
The message you should see is just "You have been logged out" and that is it.
It cannot be called as Async as there is no response from the server, unless you use PostLogoutUri which is the correct way to handle this. This will be already available in the next version: TSphinxWebLogin: Add LogoutAndEndSession overload with post_logout_redirect_uri support