I've had issues in the past where all scheduled searches carried a warning like "this schedule was set in Japan Standard Time, but when you save will be in [local timezone]"
Also iirc, scheduled searches don't adjust for Daylight Savings Time. i.e. if you have a search scheduled for 23:30 filter for "Today", when DST comes around you may find it's now scheduled for 00:30 and the filter for "today" means there are no results (ask me how I know 😏)