"(1) Is this a question of aversion? How can I avoid being phased by negative states?"
"(2) More specifically, how do I avoid identifying with such negative states, and how do I recognize their impermanence when they occur?"
Here, I think @Lanka and @ruben2020 answered these.
"Basically, I know one ought to observe such states mindfully, but in their immediate occurrence I get caught up, I am motivated to act or speak in a negative way."
When one easily gets caught up and have a hard time being mindful in these circumstances, I believe one particular problem might be weak samadhi.
When samadhi is practiced, when tranquility and unification of mind is a bit more developed, there's a natural "delay" when unwholesome states such as anger arises, and there's a natural inclination for rejecting it.
By "delay" I mean, instead of being taken by it at the spot, one sees the anger arising. Not only does it feel "slow", but it also feels detached, "far away". Feeling detached, and "far away", one notices right there that it did not invade his mind -- though it is right there in the "vicinity".
And at that moment, it's as if it needs one's decision and active engagement to make it grow. If on previous occasions one would be taken by this sort of state almost instantaneously, now it requires effort to be taken in, though one may still be seduced to engage.
Against that seduction, one notices the natural underlying inclination to rejecting it. Perhaps because samadhi is found in one's mind at that moment, perhaps because one can bring to mind and remember what samadhi felt like recently and one instinctively (or objectively) knows that engaging in these negative states of mind sacrifices that very wholesome state. Be as it may, it's a precious thing to sacrifice and likely one can feel it.
In other words, and to put it simply, when samadhi is made stronger negative states are made weaker. When samadhi is stronger, it becomes harder to engage in them, it's naturallyunwholesome states. It's naturally harder for them to invade the mind without having to make any special effort at, in the sense that momentit doesn't require special efforts to oppose them, as it would otherwise.