Anti-Static Soldering Mat - Makes hair stand on end?
An anti-static mat should have a connection point where you can tie it to ground to bleed off the charge. 

The mat you linked to does not seem to be a true anti-static mat, but rather a silicone heat insulating mat.  It says it has anti-static properties, but doesn't have a ground connector and does not specify exactly what those properties are.  I personally would not trust it.

From one manufacturer's instructions:

GROUNDING:
Sufficient ground cords should be used to reliably meet EN 61340-5-1 Table 3 less than 1 x 109 ohms for working surfaces. Industry recommendation is that continuous runs of ESD matting should be grounded at 10ft intervals to allow proper charge decay rates. Each individual ESD mat should be grounded with ground snaps located no further than  ve feet from either end.