Question:
If a person works from 12am - 8am one day, then is told about a schedule change and that SAME day starts a shift at 11:30 PM, are they required to be paid overtime for the 1/2 hour within the same 24 hour period?

Maybe yes. Maybe no. The issue is that "schedule" and "schedule changes" are legally meaningless. Overtime is based on something called the "workweek", which is legally unrelated to shifts and schedules. It is possible for employers to have more then one workweek, although practically speaking this would be very unusual. My last 4 employers were based in CA and all 4 of them had workweeks that ended Sunday midnight, even though these were all pretty large companies with many shifts and schedules, almost all of which did not end at Sunday midnight.

Your employer gets to pick what it wants it's workweek to be but once this happens it is very legally difficult to change it later. It is extremely likely that they do not change the workweek every time someone's shift or schedule changes. You need to find out what your company's workweek is. Past that, it is like dealing cards. If the workweek ends at Sunday midnight (for example), then the workdays also end at midnight. If (for example) Bob works 8 PM to 5 AM (1 hr lunch starting midnight), then legally he has worked 4 hours in two different workdays.

http://www.dir.ca.gov/dlse/FAQ_Overtime.htm