Like I said, some people experience the smell and some don't. I'm in the Mustang arena and it is a common complaint with "Peel n Seal" or "Peel n Stick" from the local box stores. A google search for Peel n Seal and smell will give mixed results, some complaining about the smell for months and some saying it doesn't smell. It also will show people complaining about it not sticking after a few months installed (DIY and professional installs), while others say it's been on for a few years and hasn't moved.
By the way, Peel n Seal/Stick is definitely asphalt based and is intended for weatherproofing horizontal roofs, not automotive sound deadening. It just happens to be similar to automotive sound deadening and is cheap.
From their website:
Peel-N-Seal is a 40 mil. thick waterproofing membrane consisting of a self-adhering rubberized asphalt laminated to a high density polyethylene film. A special release liner prevents the membrane from sticking to itself in the roll. The heavy polyethylene film is resistant to cuts and tears while providing excellent waterproofing characteristics.
Also:
http://bma-sales.com/pdf/peel-n-stick.pdf
To minimize an argument, yes it works and yes people have gotten good results with it. It is thinner than the products made for soundproofing and doesn't sound proof as good as the thicker stuff. Ultimately there are better alternatives to peel n stick, but it all comes down to the budget and what your goals are