Al,
The Timezone should be able to be set by the owner
Perhaps we could suggest that a member timezone be one of the settings the admins (owners/moderators) can make in the Def Sub Settings tab of the group Settings page.
If the joining member hasn't already set their timezone (in their account settings) then it could be pre-set from this default member value.
If I have no control over the individual users Timezone
Then the messages will be 3 hours off for everyone and
confuse the posts as to the request and what is the actual
time and when the request is due
I'm not sure what you mean by "the request", but message content (a time written in the body of a message) is never adjusted for timezone. So if you are posting instructions with due dates and times, those won't be affected.
The member's timezone affects what the member sees on the web site as times that messages and other content is posted, and events in the group's calendar. When the member first signed up and logged into the web site they had the opportunity to set their account timezone. If they're looking at the group calendar there's a control there to set the member's account timezone also. So for most members this won't really be an issue.
At one time it was said that on that first log-in the system would automatically detect the member's timezone and set it accordingly. I can't easily test that (I'm in US. Pacific time) so I'd be happy to have someone in another timezone confirm or deny that for me. Note that means the first log-in of a given email address. If Groups.io has ever seen the email address before (joining your group or any other) then this does not apply.
However Digests are the exception - members might be email-only, receiving Digests without having ever logged in to the web site. So to handle that case having a default timezone set by the group admins may be beneficial.
Shal