If I understand correctly, this is controlled by whatever timezone is set on the phone or tablet? My phones' timezones get updated automatically when I travel but my tablet is always set to the original timezone. Thus, i need to log into AnkiWeb from my computer in the timezone I currently am in and "reset" the scheduler?
Also, since I am already running Anki 2.1.15 on my computers I do not follow your comment on switching to a new scheduler - could you please elaborate? Is this not the latest one?
The 2.1 scheduler is an option in the preferences screen. You may run into issues syncing devices with different timezones however - the 2.1 code was written with the assumption that all devices would be in the same timezone. If you don't want to adjust your tablet, I'd recommend staying with the old scheduler for now, and adjusting 'new day starts at' to 4am on your phone each time your move to a new timezone.