Hi,
I can only speak from my own experience but I found that the biggest factor was actually very tiny differences in finger placement.
When I started out my fingers seemed way too big and fleshy, but they just seemed to get smaller with practice.
Calluses and a lighter touch certainly help, but if I press down really hard now the strings still mostly ring accurately.
What seems to have changed over the months was a series of very tiny subconscious adjustments until my fingers could feel exactly the best spot for the string to be touching the tip. Eventually both the brain and the fingers seemed to work out the right spots and angles, and also actually be able to reproduce them again next time around.
An interesting trick is to try playing a mandolin for a while. They have fretboards about the size of a toothpick and appear to be made only for elves to play.... But after a while you can even get them to work. Then when you go back to guitar the neck seems as wide as a freeway!
Cheers,
Chris