(How) do pilots round the time?
The roundings I know of in the context of US general aviation aren't strictly defined or enforced because they don't need to be (with the exception of racing; see below). The military might need to be more precise, but I have no idea about that.

Anyway, here are the main roundings a typical GA pilot might encounter:

Logging: to the nearest 6 minutes

Pilots usually log their flight time in tenths of an hour, i.e. they round to the nearest 6 minutes. There's no regulation on it and some people prefer to log in hours and minutes (maybe it's even required in some countries), but tenths seems to be most common.

ATC instructions and clearances: to the nearest minute

See this question for information on timing under IFR (some of it applies to VFR too); instructions, clearances and reports are given to the nearest minute. It is required to have a clock with a second hand but that's to make it possible to do timed turns, not because ATC gives instructions down to the second.

Air racing: to the second or less

In air racing, there are at least two ways of using time. In a speed race - like the Red Bull Air Race - you measure the elapsed time over the course. The timing for Red Bull is to one thousandth of a second.

In precision navigation air racing, you plan your flight over a specific course and calculate the time (and sometimes even the fuel) you'll require to fly it. When you fly the course, any deviation from the numbers you submitted beforehand - under or over - is penalized. Timing in those competitions is to the second.