1. The 'Yesterday" and "Today" timestamps appear to be working on the server date/time rather than the site-adjusted offset date/time. When I commented-out the 'Make relative date' calculations in class_global and reverted back to normal, the 'normal' timestamp correctly adjusts for the offset.
2. The above is not the case with messages between members, which are timestamped with the server time and not the offset time.

Thank you for having a hawk's eye! Registered, and on the list of stuff to fix & improve.