No, it sounds like you are fine

Like you say - different people have different ways. But I think it depends on the circumstance too.
For instance, you were a trained first-aider. Perhaps you never expected to have to use it, but you had a set of protocol to deal with it and you were prepared for the eventuality to some extent.
What I found so difficult about my reaction was that I really thought I was unshakable. I'd seen some pretty unpleasant things in the past. I lived in a post-conflict country and saw rooms of preserved dead people, kids with pretty yucky diseases, people with fairly awful disabilities and scars (such as a guy with all four limbs removed going about his daily business with flip-flops tied to his knees).
I really, honestly thought I had a fairly un-shakeable constitution on that front.
But like you, I'd spent months preparing for it. I knew what I was going into. I'd watched the films, read the books, spoken to people and I had a network of friends and colleagues in the same boat.
When the crash happened, I'd just driven my friend home from work and we were sitting in her front room in the early hours (she works in a bar). I was just about to leave when we heard him coming.
I think it was because I was home, in a 'safe' environment, a little village where nothing ever happens. There was absolutely no reason in the world to expect or prepare for what was about to happen. The mere fact we heard him was enough to make us sit up - you don't even get boy racers around there.
In addition, the things I'd seen before were old wounds. The people had been dead 15 years, they looked more like papier mache than actual people. There was a distinct sense of un-reality about them.
This was just so very immediate. It was right there in front of me in a place where I would never have expected to feel that 'high alert' feeling. One second he's alive, less than a minute from home, the next second he's dead. That quickly.
Even so, I'm surprised it's got to me as much as it has. I followed up by ringing the church bells for his funeral and watching the service from the back. The funny thing was, he was 19 but he'd already told his family that if he died, he wanted a poem read out. Oddly, it's the one TAK has on his signature: "'Do not stand at my grave and weep..." Strange he should think to say that in such a way his family would remember.