Probably related to French tamponner ("to plug or stop"). See tampion.
Full definition of tamp
Verb
(blasting) to plug up with clay, earth, dry sand, sod, or other material, as a hole bored in a rock, in order to prevent the force of the explosion from being misdirected.
To drive in or pack down by frequent gentle strokes; as, to tamp earth so as to make a smooth place.
