Mat's amulet did not protect him, because the lightning drawn against him was basically electrical energy that was taken from the environment, and thrown at him in a bolt of energy.
The closest examples of this in real life is a model railway and the electric fence on a farm. The electricity that allows the locomotive to move is done in pulses along the track and the farm fence is exactly the same, but a far stronger pulse.
If you put your finger on the model track it will get a shock just before the locomotive touches it, and it will tingle. The pulse from an electric fence, by comparison, will throw you a few meters from it in a shock.
Exactly how Elyane will throw rocks at him on the way to Ebou Dar, and as you said, Adeleas and Vandene threw horse manure. What they were all discovering, Rahvin already knew what was happening, and knew ways of how to counter it.
His expertise in the One Power allowed him to do that. Mat's amulet will only protect from direct weaves trying to do something at the touch of his body.
It will not protect Mat from any elements that weaves generate before triggering the process.