A minute is still 60 seconds. The only difference is that some clocks will occasiomally go an entire minute without incrementing their minute counter. This is a property of the map, not the territory.
You're choosing to define it that way when the entire point made here was that other people can and do define it other ways.
They change the duration of the day, not the minute.
The clock goes from 59:59 to 59:60...
Yeah. Or they smear it over a longer time period, but that still (slightly) extends the duration of each minute.