Nice bit of video. Good to see a sand tiger in action like that.
Sand tigers are called grey nurse sharks in Australia and probably have similar behaviour as they are the same species - they certainly look and seem to behave the same from video and photos although I have not dived with them off the USA.
The video looks to me like pretty typical behaviour for our sharks. The shark gets a bit close to a diver and then makes a sudden turn and swims away. Sometimes the turn is so fast the tail flicks hard enough to make a sound like a cracking whip. Impressive to see and hear, especially if it's a big big shark doing the turning.
In Australia, these sharks tend to swim a fixed pattern during the day along a reef or around a gutter. Sometimes it is a circle or figure 8 around quite a small area of reef. If you get in their way they seem to approach very close then suddenly turn, almnost as if they are in a daze or asleep and suddenly wake up to see you they (apologies for the anthropomorphism). This has happened to me a few times accidentally even though I feel a bit guilty about disturbing these sharks normal behaviour. However, I have not heard of anyone being bitten in this situation, so I am guessing you were not in any danger, although it is probably a good idea to be extra respectful of any animal bigger than you are.
Once I accidentally did sort of block a 3 m + long shark in a corner of a reef while concentrating on photographing something else. I looked up to see this shark approach as you must have done. I just couldn't move out of the way in time. When it got to the point where they usually turn, it just stopped and really seemed to glare at me for a few seconds before turning away. I think I must have really annoyed it, and I probably deserved to get bitten. Still didn't happen. The only people I have heard of that get bitten by this species are those that grab on to them as they swim past- but can't really confirm the accuracy of these stories as I have never seen it happen myself.