After today, I realized that some proxy server really sucks. I had designed that my public web server will redirect all unsecured web traffic via port 80 (http) to a secured port (443) with encrypted authorize global SSL certificate.
The redirection work perfectly fine on desktop IE, Firefox, Chrome and Safari over public Internet. Major device os such as Android and IOS apple, also work perfectly without any nag of untrusted certificate issue. Well there is nothing can do about it for time being.