“Does God punish people with earthquakes?” someone inquires. The short answer is, “Yes,” but some clarification is necessary.
God created a perfect world and an Edenic habitat for the original pair of humans, Adam and Eve. However, once they sinned (Genesis 3), God modified His created universe. Adam and Eve were expelled from the Garden of Eden, in which they had access to the Tree of Life, by which they would never have died. Consequently, death entered the world, along with its accomplices—aging, pain, diseases, accidents and murder (Genesis 4). The earth underwent changes, too, with the introduction of thistles and sweating labor; these may be representative of other changes from paradise that we experience today, too.
Later, mankind excelled in sinfulness, for which reason God determined to destroy the surface of the world that He had created. A remnant, though, of humanity—Noah, his wife and their three sons and their wives—was spared from the universal flood (Genesis 6-8). Only eight people and a sampling of animal kind aboard the ark (barge-like ship) survived that deluge (1 Peter 3:20). The events surrounding the flood forever changed the face of planet Earth as well as its weather patterns. Continents may have formed; mountains and valleys occurred; global weather dramatically altered from what it was. Thereafter, natural disasters such as earthquakes, hurricanes, tornadoes, local flooding, snow blizzards, droughts and such like were commonplace. Akin to that, disease, genetic defects and similar maladies also became ordinary.
All of the foregoing and kindred things represent changes that God made to the created universe, including our world, as a consequence of human sinfulness. In that sense, God punished and started a process that continues owing to sins by His highest creation—man. However, God does not punish, today, anyone or any portion of the human population directly through natural disasters, such as earthquakes.
This is what we can discern from Scripture and observance of the natural world in which we live. If God were to punish anyone in our day with earthquakes or other natural disasters, we could not distinguish it from what He has already set in order because of the entrance of sin among men. If God were to punish anyone or a segment of the world’s population with natural disasters, such as earthquakes, He would do so unseen and through the behind the scenes working of His providence.
Essentially, mankind is responsible, because of sin in general, for the presence of natural disasters, death, aging, disease, etc. However, we have no evidence that God is presently targeting anyone or any group of persons in particular with catastrophes (i.e., earthquakes, disease or even death).