A person's personality is not a part of how he acts but to use a Butchism, his "body of work." I see Coach Jones as being intensely genuine and passionate regardless of what he is doing.
It starts with his enthusiasm and approach to recruiting and his sense of the every player as a family member and to making sure that each person be successful at getting a quality education. We know how passionate he is about family.
Then on the field, there is a different kind of passion. I believe he believes that it is a privilege to be at Tennessee with its traditions, educational opportunities, and outstanding football facilities, so what is a player waiting for? I can see that he would nitpick, criticize, blapheme, and calls out players -- and coaches -- for not having his level of intensity which he feels is necessary to achieve their goal. Really, I doubt if few has his intensity. Everyone has to perform at the highest levels all the time to get to where everyone wants to go. And it cannot happen without relentless hard work. Then now one is prouder of the team's accomplishments than he is.
I don't see it in terms of self-aggrandisement either. It is legitimate pride in the young men who achieve their goals. With Butch, a person is all in or not in, there are no degrees of being part of the program. After the rant as is his personality type, he is just as quick to praise. He said it is just like being happy about the accomplishments of one's own children. So he is passionate in selling UT to recruits, passionate in coaching hard and being hardnosed, and passionate about the accomplishments of individuals and the team. Collectively, that is his personality.
Personally, I don't see any dichotomy here.