In the same chapter "Zeus and the Earthquakes" of Zeus: a study in ancient religion, Vol. III, by Arthur Bernard Cook, quoted by @sand1 in his answer, the author says:
In point of fact, the earliest extant description of an earthquake
attributes the phenomenon, naively enough, to the action of Zeus, who
nods his head, shakes his hair, and thereby makes the mighty mass of
Mount Olympos to tremble.
Indeed, Homer in the Iliad tells us this about Zeus:
The son of Cronos spoke, and bowed his dark brow in assent, and the
ambrosial locks waved from the king's immortal head; and he made great
Homer, Iliad. 1.528
But, as you already mention in your question, Poseidon is called "Shaker of Earth" more than thirty times in the same work.
I wouldn't discard an earlier association between earthquakes and a chthonic Zeus but, during the classic period at least, "the Shaker of Earth" was definitively Poseidon.
Then, as @sand1 mentions in his answer, and quoting again from Zeus, a study in religion:
The fact is that, as the centuries went by, Poseidon lost while Zeus
gained in religious significance. Earthquakes came to be connected
less and less with the former, more and more with the latter.
The author then mentions a series of earthquakes, with the first examples attributed to Zeus dating from A.D. times.