This is for Switzerland (SBB):

Let's say, we have departure time 08:02, the driver (if single operation), or the conductor gives the command to close the doors at 08:01:50, and the departure signal gets switched on at 08:01:55. That means that the train starts moving when the minutes hand of the clock jumps to (08:)03, and the seconds hand of the clock gets released.

Arrivals count as "on time" if the train stops not more than 3 minutes after the arrival time listed in the service timetable.

From reading, on certain lines in Japan, a train counts as "on time" if it stops not more than 30 seconds after the time listed in the service timetable, which does list times not just as hours:minutes, but hours:minutes:seconds.

Such a punctuality is an absolute necessity when the line is operated at full capacity (let's talk 30 trains per hour and direction or more.