I don't have experience with their product, but their web site claims it is not asphalt based. From this I assume* it is a butyl based product, which is generally a superior product to asphalt.[*] you really should check since they didn't come right out and say butyl, and assumption can be a dangerous thing.
Just to clear up a couple of points. This genre of product is known as a sound damping mat. It uses mass (weight) in a viscous material to dampen vibrations - not deaden sound. Sound deadening (maybe should be called sound adsorption) is accomplished through the use of jute like mats or a closed cell foam product (think neoprene, Ensolite, etc.).
The HushMat may end up producing a quieter vehicle through reduced vibrations of panels, but if your goal is seeking Lexus/Cadillac type quiet, then you need to pursue the closed cell foam/jute addition to the HushMat as well.
The addition of a square foot of closed-cell foam mounted to to the inner side of the door outer skin - directly behind door speakers - is well worth the effort. Yours ears will have more appreciation of the bass notes coming from your speakers.