Exactly; squarely; precisely. Saying something is "on the nuts" is akin to saying it's accurate and "on the mark." The phrase arises out of the experience of getting hit in the nuts, which, when hit exactly or squarely on the nuts, is much more significant than otherwise. Thus, you say something is "on the nuts" when it is exact and precise.
"What time did you get there?" "7 o'clock, on the nuts."