If an underground aquifer/reservoir doesn't have water in it, the ground surrounding the area would start shifting, and lead to the rumbling. It's a good coincidence that the earthquake/rumbling started right as Mac arrived, but I assume the pumping had been going on for a few hours or days before Macgyver's arrival - which would have caused the aquifer/reservoir to already be partially depleted.
While I am not a geologist, I assume the technical term would be similar to what is described here -
https://en.wikipedia.org/wiki/Groundwater-related_subsidenceI think the plot of the 007 movie "A view to a kill" from 1985 involved pumping water out of an underground reservoir and starting an earthquake - and while the plot of that film involved a bomb as a catalyst device, Macgyver could have got the idea from there, since we know he is familiar with James Bond films.
In addition, here are a few articles involving drilling the ground and leading to earthquakes.
https://www.latimes.com/local/lanow/la-me-l...0514-story.htmlhttps://www.scientificamerican.com/article/...ng-earthquakes/