I think a stopwatch is a different beast from 0-based or 1-based indexing. A stopwatch is used to measure the time interval between two events. If stopwatches could somehow magically measure and display time in infinite precision we wouldn't have this discussion. But if they do rounding to the nearest displayable number then they display 0 for half of the time-step interval, then display the subsequent numbers for the full time-step interval each.

I vaguely remember that the original minesweeper started counting time from 1, which is certainly odd. I could be wrong here though.