Similar to the DO weakening the Pattern, his touch spoils things, dramatically changes the weather, increases vermin, etc., in order to basically create a global Blight, which kills humankind.

However, Rand's state and connection to the land can apparently reduce (but also strengthen) this effect. The damage is apparently also reduced by giving order & belief to the people. Factors like the Tinkers' firm peaceful belief might actually weaken the Shadow. Therefore the Tinkers were IMO also the actual target of the Trollocs seen in TGS, prologue, which coincidentally bumped into Tylee's Seanchan army.

It seems very likely that the Tinker will help to heal the world after TG (some suggest that Aviendha might find the Song), though I think the most dramatic changes (e.g. the darkening the sky) will immediately be reversed, when Rand defeats the DO. We also saw the Blight immediately receding after Rand's victory in the end of EotW.