We are dealing with this same issue on the Project level. An user will
attach a task template and all tasks correctly adjust times based on the
default 9am-5pm schedule. But as soon as the user, who is in Eastern
time zone, it defaults to 12AM local time and therefore all of the tasks
are reset to 12AM ET on their respective days as well. Users in Central
time then see due dates on the day before since they are shown one hour
earlier (11pm).