The Pay Period configuration has a Midnight Offset setting. By default this is set to 0:00, but can be changed when needed.
The reason to use a Midnight Offset is when a company has a shift that starts near midnight and they need to ensure that the work time of the shift is considered part of either the previous or the new calendar date.
For instance, if you have a shift that should start at midnight and is part of the new calendar day, but your employees might start clocking in as early as 11:30 PM then setting a -0:30 midnight offset would be appropriate.
On the other side of the coin, if your shift starts at 11:30 PM and you want to ensure that anyone who clocks in late (even after midnight), still get their time applied to the previous calendar date, then a positive midnight offset is appropriate, like the 0:30 you had in place.
Example:
With a Positive Offset of 0:30...
Any shift that starts between Sunday @ 12:30 AM through Monday @ 12:29 AM will be considered part of the Sunday calendar day.
With a Negative Offset of -0:30...
Any shift that starts between Saturday @ 11:30 PM through Sunday @ 11:29 PM will be considered part of the Sunday calendar day.