Editing the same Alert will show two different times in the schedule/"Time of Day" depending on Local System Time. I would suggest using UTC.
My PC is in Central, the APE is Eastern. My Web Session shows Eastern (Top Right Clock).
The Alert took the time input 11:00 PM - 4:00 AM as Central from my PC. Going to the APE and editing the same alert now shows 12:00 AM - 5:00 AM.
The Web Session time (Top Right) leads one to believe this is your reference, but it's not. I would suggest using UTC and labeling this field.
Thanks