When setting a send date in messages, the send date does not respect the time zone of a user as it appears, but does when sending the email. For example, a user set to PST, on a site set to PST, sets a send after date of 4 pm on an email. A user set to EST edits the message and the send after date will continue to appear as 4 pm. If this EST user sends the message though, it will send at 4 pm EST rather than 4 pm PST.
We are currently evaluating this issue and will update this article when we have more information.