Like a wave. Many people are disturbed by such occurrences & reassurance that this is normal (it is) often helps. The worry itself can make it worse sometimes. The fight or flight response triggers rapid shallow breaths which trigger a cascade of physiologic changes like the ones mentioned. Focus on your breath and intentionally take longer breaths. Think of the anger like a wave that crests and dissipates.
Adrenaline effect. The response you describe is unusual, but probably caused by release of adrenaline, the fight or flight hormone. People notice the same after 'near miss' car accidents, where a few minutes afterward, the body starts shaking for a few minutes. The cause is the same-- a rush of adrenaline that makes the muscles shake. Beta blockers will stop it, if it becomes a problem-- or avoid angry situations!
It can happen. When you are upset, your body makes more adrenaline, and that can make you shaky.