According to Wiki, it was more complicated than that. Pumice buried most of what was left on Thera. Not enough ash descended on Crete, but with such a cataclysmic explosion of the island, a tsunami probably devastated much of the infrastructure on Crete. Weakened them, and Mycena invaded.
That’s the basic nutshell version.
I’m inclined to think that Crete was the hub and Santorini an outlyer. If I remember correctly, Akrotiri was probably abandoned about 20 years earlier because of severe earthquake (preliminary to the big explosion). I believe that the major tsunami destroyed the shipbuilding coastline of Crete, and killed many of the shipbuilding craftsmen. Thus, although Crete did not fall immediately, and ships that were at sea came home, all efforts would have concentrated on repairs, and very little on building new ships. Thus, severe social dislocation, trade difficulties, loss of income and vulnerability to attacks from within or without, and the subsequent signs of burning and other disorder. As a separate thought, I think part of the artistic creativity and freshness described for the new monotheistic city, Amarna, in Egypt was because they hired refugee artisans from Crete.