"Asphaltum" is somewhat of a catch-all term, especially nowadays. Historically it was generally referring to a fossilized resin, not a fresh or sticky tree resin. For those who appreciate this type of finish or coloring, you can obtain a darker color if you dissolve the resin into heated turpentine and use that as a 'stain' followed by either oil or - as Wallace uses here - resin dissolved in oil. Red maple in particular, due to the easier penetration of the the wood, can yield very dark almost black stripes with the resin in turpentine as it will penetrate more deeply into the wood than when oil is used as a vehicle.
The HUGE benefit of this type of finishing is no grain raising whatsoever, always a detriment to using aqua fortis.