I think a good way to begin to answer this question is actually by emulating many, many people and having many musical (and other) heroes, over a long period of time. Tony Williams said that he tried to play exactly like Art Blakey, Philly Joe Jones, Max Roach, and others when he played along to records. By trying to cop not just the notes, not just the phrasings, but the FEEL of his heroes, he came up with his own feel in the process. He was being intentional, without trying too hard. Likewise, Vinnie did everything he could to play exactly like Tony, Billy Cobham, Elvin Jones, and others, and yet he came up with his own distinctive feel as well.
The key here, is that it didn't happen overnight, for anybody. All of the greats practiced their butts off, and not just the technical side of things...Jeff Porcaro was a great example of someone who emphasized the groove, the nuance, the tension and release of playing great music.
Vinnie himself said once in an interview, IIRC, "Before you can play for the music, you have to WANT to play for the music." Every unique musical individual has that attitude.
Sorry if I'm rambling a bit, but those are my thoughts.
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