Yes, the res phosphorus did react with the air, I checked a few MSDS, and the results for autoignition temperature vary from 280-300 degrees celsius, that would be in keeping with the occurence of varying polymeric forms of the red allotrope of phosphorus.
The dark crap will likely be caseine gum from the match boxes (If my intuition about where the red P came from, and its use is correct
left, because of the fact that the HCl boiled off perhaps, before it could hydrolyse all the caseine, also, I would be careful giving MBRP a HCL boil, because some of the strikers contain antimony trisulfide as an ingredient, which would give extremely toxic hydrogen sulfide gas when heated with acids.
The fumes, if they had a nasty, garlic-type of smell, are indeed toxic, it would not do, to make a habit of inhaling phosphorus oxides, fortunately, red P burns in air, mainly to form the pentoxide, which is one of the less unpleasant ones, but definately, do not inhale oxides of phosphorus, most of them are highly toxic.