The trouble is that android assigns a fixed time zone to all calendar
times. By default this is the time zone you're in when you assign the
time, but can be set otherwise. When you change time zones, the due-
date times android gives are the times in the original time zone after
adjustment to your new time zone. Probably not what you expected or
wanted.
You can check "use home time zone" in the native calendar (or
calengoo, but not business calendar) to make the calendar app adjust
the due times back to the original time zone. You can't do this in
mlo, so all your task times remain in the original time zone, and then
android adjusts these to the time zone you're in.
Not a solution for mlo, but at least you'll understand how the times
are shifting. The times should display correct when you're back in
your home time zone.
An alternative is to turn off the automatic time sync for your phone
and make it keep operating in your native time zone, but then your
clock will be off.
-Benton