Which came first: tone or timing?
It matters only when we try to separate the two, customarily for pedagogical purposes. "Count!" What a demeaning directive, if you stop to think about it. Surely the child can count but, as one of my astute nine-year-olds put it, "I can't count and play at the same time."
Two things come immediately to mind :
1. The teacher inferring that it is easy to count and play at the same time is unable to discern the movement that is actually impelling the student's auditory and physical coordination at the instrument. I was a student who could not play the piano and count at the same time. I would have given anything to master that skill. Teachers who insisted on counting as the solution only made things worse.
2. The artist striving to pierce the mysteries of Schumann, Schubert, Beethoven, Haydn, & Co. is hard put to overcome the habit of assuming that the quarter note (and its arithmetical subdivisions) conveys the unit of true rhythmic vitality. I am a mature artist whose astonishment grows every time I confront a composition that I had previously striven to master by counting it to death. At the moment it is Schubert Impromptus: The magic of playing multiple triplets as sextuples (i.e., in hemiola -- remember him?) is literally transformative.