I'd say "Exactly", but in casual speech I would expect this to mean "exactly nine o'clock, give or take two or three minutes." If I were expecting to hear a precise time, I would expect to hear "at exactly nine o'clock", or "at nine o'clock precisely".
There are a few other phrases that use on like this:
He went out going on nine o'clock last night. -> some time, but not that long, before nine o'clock.
Went out on the dot/stroke of nine o'clock last night. -> exactly as the minute hand of the clock reached 12.
So if we look at "Went out just on nine o'clock last night." we have a use of 'just' that indicates the minute hand having 'just' reached 12.
However, and this is where I am close to velisarius's meaning, human beings are rarely able to state time with absolute accuracy; they look at clocks and watches that might be a minute or two fast or slow. therefore, "exactly nine o'clock, or one minute to nine o'clock."