Your connection is not private on some site after security update

I have mac mini and OSX version 10.9.5. Since I update the security update (Security Update 2015-004 Mavericks) on 4/8/2015, I got "Your connection is not private" when I browser a lot of sites, i.e. https://twitter.com, https://appleid.apple.com, but no problem on gmail.com or youtube.com. Moreover, when I connect to App Store, I got "Connection Failed" when I login. Does anyone has the same issue? does anyone know how to fix it? Thanks