Remember that the mat has a pretty high resistance to earth, many megabytes. This is to leak static away rather than short it hard to earth. Shorted static is likely to damage something its charged up on, such as when a board with a static charge on is dropped down on the mat. It also makes people jump. So the mat is not a sheet of earthed tinfoil.
Therefore the tracks on your board that touch the mat are touching a large resistor to earth. I would say that the impedance between V+ and earth on your board there is pretty low because of a lot of decoupling capacitors across the rail and a lot of conduction paths, some resistive. So the effect of touching either rail to the mat produces a series circuit with the impedance to earth much higher than the impedance between the tracks. Nothing dramatic happens.