In the am/pm clock system, when written digitally, they count from 1 to 13 instead of 0 to 12. This means that 0:30 am is not valid. It should be written as 12:30 am. Only when 13 is reached, it turns into 1.
So the digit flips at one o'clock, but the am/pm switches at midnight and midday, which is an hour earlier.