SYSTEM_TIMEZONE is used to inform EPESI what is the timezone of the server. It's useful when you've done some migration to the other server with different timezone. Every date should be stored in the server timezome.
But as you can see below, during creating a new shoutbox message timestamp is not supplied, and during install field is defined with 'posted_on T DEFTIMESTAMP', so it should assing always 'NOW'... but it won't be affected with the SYSTEM_TIMEZONE setting, because SQL returns current timestamp.
DB::Execute('INSERT INTO apps_shoutbox_messages(message,base_user_login_id,to_user_login_id) VALUES(%s,%d,%d)',array(htmlspecialchars($msg,ENT_QUOTES,'UTF-8'),$user_id,is_numeric($to)?$to:null));
I was trying to reproduce your issue, but without a luck. Maybe I've got something wrong, but reading a code I think that it may be buggy, but I can't get the wrong time.
Regards,
Adam