The mat you purchased is vinyl, not 2 layer rubber. Meaning it will dissipate an ESD charge just fine, but it's not suited for use around a soldering iron or sharp objects like the 2 layer rubber is (it's not cheap, but you way overpaid for that vinyl mat).
If you mean to solder on it, here's some 2 layer rubber types on
clearance; also a good
eBay seller (lots of options here besides size; texture, color, just mat or kit,... ; also does custom sizes if you need it). Bought from both places with no problems.
Also, here's a
2 layer mat kit from Amazon (size = 24"x48"; and it's even $0.50 less than the mat you linked
). Almost certainly the easiest way to go at this point, assuming you can return the existing mat.
As per smell, both will stink initially, and the rubber is worse IME. Leaving it in a well ventilated area for a day or two will really help (likely not gone, but quite tolerable), and it does continue to dissipate over time (smell should be effectively gone by ~4 weeks or so indoors).