Oh I’m sure that you did the right thing by jumping off - by the time you noticed it, he was down. With experience, things won’t seem to happen so very fast. I remember when I learned to jump, my instructor was like, don’t forget to do x,y,z,p,d,q and I thought “when? the jump happens in an instant” but now with experience it feels like I have as much time as I need to do all sorts of things while the horse is in mid-air.
You’ll also develop awareness of your particular horse’s habits and quirks, as well as their body language, and so you’ll get a LOT more warning about what they’re going to do.
Just make sure that whenever your horse does something bad - even if you get scared or intimidated - you never just stop working immediately afterwards. That is a reward and will encourage him to repeat the behavior. Make him work on your terms, even if that just means walking him once around the ring before you dismount or even getting off and leading him round the ring if you aren’t feeling safe.
Horses are basically lazy and you never want him to think he can end the work by misbehaving. Horses will test you and see what you will and won’t accept (especially those wise souls who are beginner safe). The one exception is if you actually get angry and start to feel out of control. In that case, separate yourself safely until you feel calm again.
On the flip side, be free with immediate rewards and encouragement when the horse tries do as you say, even if he doesn’t get it 100% right. You my not feel much like a trainer right now, but every time you work the horse, you are training him. You are establishing a pattern of behavior.
You might consider some basic “clicker training” also known as operant conditioning as something to try in the winter months. The best thing about it is it “trains the trainer” - it will focus you on your horse’s behaviors and reactions, at the same time it focuses the horse on you and what you want. One winter in Michigan, when it got so cold the indoor arena froze, I tried it and I learned a lot from the experience - even though the only thing I taught my horse to do was touch her nose to a target.
Working with horses is amazing, infuriating, fun, frustrating, inspiring, and confounding, all by turns and even in the same 15 minutes! Good luck!