There's no secret.
I love baseball. Most of my analogies go back to baseball.
I HATED the first few weeks of baseball practice. Why? Fundamentals. My father was my coach.... and he was no joke. He would hit ground ball after ground ball at me at a zillion miles per hour. "BEND YOUR KNEES! GET IN FRONT OF IT! LEAD THE BALL!!!"
Why do you practice every tiny little detail of your swing when hitting?
Now I get it. You pound the fundamentals into your head, and muscles, so that when the ball is hit, you don't HAVE to think. You FEEL. You almost SMELL where the ball is going. Your body just goes where the ball is. And you get in front of it. And when you stop it, you take one hop and you GUN it to the cutoff guy without even thinking.
The same goes for music. Do the math during practice. Learn theory and chord structure. Practice scales. Practice arpeggios.
But when the drummer clicks four times, STOP DOING MATH! The math is already in your head. Just feel the groove. Just go where the rest of the band takes you.
Make no mistake. Even if he has no formal training, he knows theory. He has practiced, and practiced, and practiced. So much so, his ears know what sounds good in a given situation.
Short version: Work the fundamentals. Then let go of your head and feel the groove in the band.