Gosh...makes me feel good to have someone ask me a question!!! smile... It's even one I can answer - and thanks!
All of the War Diaries of Dad's ship show the time zone..
At the beginning of each month's Log, after the From, To, Subject and Reference (their current orders), and on each subsequent page they show Zone -11 (for example). As they traveled into another zone, you are right - it shows "Set all clocks back (or forward, whatever the case) one hour to conform with -10 zone time."
For the Operational Remarks (War Diary), at the top of each day's page it shows "Zone Description". At New Orleans, it shows +5