There's a few things going on. First, you found one - General Time Zone is set to "Set Automatically". Second, here's your PITA - if you want your meetings to "travel with you" and adjust with you, set Calendar Time Zone Support to "Off" - otherwise every calendar event will be displayed according to the time zone selected for the event (when set to "Off" the events will be displayed according to the time zone you're in. Third, if you're traveling you ought to consider enabling the "Setting Time Zone" Locations Services System Services. And, fourth - network time is pushed by your network, not the iPhone (or any other mobile phone) - if you're roaming, say on USCC and you're a SPCS or VZW customer, the network time update may not be supported on USCC - and the update may not happen immediately even if you're on your native provider, I've had updates pushed hours after the bump occurred. And, Apple may have overlooked the network adjustment in their software - they boofed a time bump a couple of years ago and it was national news.
One of the above is likely the source/fix of your issue. Also, reboot your device and/or reset network settings. And, if you're on SPCS or VZW, update your PRL (if you're in a native service area, of course) - they both had updates just a few days ago.