How did rust appear on my cast iron in a matter of minutes?
The problem with your last step was the lid, I think.  

If you had placed it on the hot coals, open, the heat should have driven the water off as you intended, drying the pot before it rusted.  With the lid on, the moisture was trapped inside, and had opportunity to cover every inch of the metal - and, as Joe mentioned, heat speeds up the reaction.  Sitting on the heat with a coating of water, and you have a layer of rust.  Not functionally different that if you'd tried boiling a pot of water before seasoning it.  The seasoning is, after all, supposed to protect the bare metal from water so it doesn't react like this when being cooked in.

How to fix it - go back two steps.  Scrub off the rust, or as much as will come off easily.  I agree with paparazzi, here, if it won't come off while scrubbing it will probably not come off while cooking - especially under the seasoning.  Once it's well scrubbed, dry it off.  You might use a towel or something first, but if you're going to put it on the fire, leave the lid off so the moisture can escape the pot.  

You might have the lid drying to the side, leaning against the outside of the pot, or partially on (generously offset) if you want to dry the lid as well.  You probably don't need to heat it for long, either, just until it looks dry - and it will be evaporating water all the way until it cools down, too.  When I'm re-seasoning my frying pan, I heat it only 10min or so, and by the time it cools it is usually dry (disclaimer, I use the stove rather than coals, so your timing may vary).

After that, you can smear it with a layer of oil and re-season.  wipe it down with oil, and heat to re-create the layer of seasoning that got scrubbed away in the first place.

Beyond that, it will probably help to calm down a bit.  In the future, just remember to keep the lid off when drying, and that you don't need to panic quite as much.  Cast iron is pretty sturdy, and scrubbing down to the metal and re-seasoning is always an option until the pot is worn away to holes.