Reminders do not print the times entered in event.
I set my calendar to AZ time and entered my times but the reminders go out with GMT time. - This is unacceptable. There should be an option that the international groups can use where the time translates to who the receiver is (like outlook) and doesn't mess with the point of origination times. Ours is a neighborhood group - no time translations are needed.
The time zone used in replies is set through the Actions menu on your group's event calendar.
That is separate from the time zone you set in your personal calendar, which is used to display events (and edit them) on the calendar.