Timezones are in like three places in osT.
My Preferences or Admin panel -> Staff -> staffs name -> Staff's default timezone
Admin panel -> Settings -> Default Time Zone
PHP's configuration file (php.ini).
It's possible that you're discovered a bug. I haven't had a chance to see if I can replicate it, but once you rule out all the settings you may want to post an issue on github.
Everything is correct except for the PHP configuration. I'm on a shared server over at HostGator which defaults to CST, and cannot be configured. Though, that still doesn't explain the time difference, as "America/Chicago" isn't 6 hours off from "America/New_York". Either way I added the following code to a new HTACCESS file in the OSTICKET root directory. Hopefully it's supposed to go there.