Okay, what you want is for the seconds to not be seconds but 1/59 fractions of a minute.
I don't know why you're not happy with the above that does it in exact seconds.
But say you want what you asked for the instead of diff.seconds you'd have to put in something like:
Math.Floor((diff.TotalMiliseconds % (1000*59))/1000);
But why you'd want this is beyond me. Try with 360000 (or 6 hours clean)
(360000 Mod 59000)/1000 = 6. So there is 6 seconds there out of nowhere!
The more time elapsing the worse this will be.
Included the code snippet you were referring to:
var days = Math.floor(distance / (1000 * 60 * 60 * 24));
var hours = Math.floor((distance % (1000 * 60 * 60 * 24)) / (1000 * 60 * 60));
var minutes = Math.floor((distance % (1000 * 60 * 60)) / (1000 * 60));
var seconds = Math.floor((distance % (1000 * 59)) / 1000);