I like to think of it as developing at least 3 separate brain areas.
One area is responsible for the tempo, meter, and my 1-2-3-4 count (or whatever time sig) This area underlies everything and over the years, has come to be instinctual.
The other area is regulated by the first area, and is responsible for my ideas, my comping, my dynamics, the grooves I choose...the majority of my playing. My time circuits are independent of this area and autonomous and relentless.
The 3rd area is an "executive overseeing" area that is listening to the entire net result of my playing and evaluating if I am too fast, too slow, too loud, inappropriate, or in the pocket. I can only access this brain area if I focus my eyes far away from the drumset and up to the ceiling. This allows me to listen as if I am not playing. This is a vitally important process for me, evaluating what I am doing, right when I am doing it, and deciding if it is on the money, or is falling short.
Of course the goal is to shut off conscious thought, quiet your mind, open your ears up, and play reactively. (talking improv here, not "frozen" cover songs) Rather than thinking of things to play from my own mind, I try and feel what needs to be played from a larger perspective.... outside of my own little mind. I try and meld with the universal musical consciousness. It all sounds New Age-y and stuff, but that's where the real beauty in music lies, beyond your ego. First you need to abandon the ego and just surrender. You aren't the river, you are the riverbed, waiting to receive and channel the great waters. (from Kenny Werner's book "Effortless Mastery")
Sorry I got off track here. Yea counting should be involuntary, automatic. But first you need to do it voluntarily, until it becomes something you can't ever stop.