It can stink for months, but more importantly, asphalt is a very poor vibration damper - no viscoelasticity. It out-gasses toxic fumes. It has a low heat tolerance that decreases with age making it prone to melting or falling off.
When looking for sound deadening mat, you want aluminum foil on butyl adhesive. The thicker the foil the better it will work. The thicker the foil the more it will cut your hands, so there is some room for compromise there, but you want foil, not some plastic or plastic with super thin foil composite.