Most people think that Dionysus, the god of wine, was no more than the drunken sidekick of Greek mythology. In fact, he was a rather powerful god who controlled the wild forces of nature. He did not care for the orderly fields and orchards of his sister Demeter (Ceres). He much preferred tangled vines, thickets and dark, dense forests, where anything might lurk, and riotous, wild vegetation growing abundantly.
That is why I think he just stopped at Delos. After sipping some wine, he left, next to the empty amphora, another trace of his presence, in the form of the wild flowers filling every nook and cranny of the island.