If a drop a water hits the pool a wave will propagate out from where the drop hit the pool of water - i.e. there will be a wave.

Suppose you`re right. Then, as reckoned by an observer on the Moon, if I tug on the Earth the effect (jolt) is felt near Mars at the same instant I tugged.

As observered from another frame of reference, e.g. a fast rocket ship whizzing through the solar system along a line parallel to the line connecting Earth and Mars. An observer in the rocket would not rekon the tug on Mars to be instantaneous. Depending on his direction the tug will have either occured before the jolt, or the jolt occured before the tug.