Mr. Isaacs is Sibyl's manager. He has lent her mother fifty pounds, a large amount of money in those days.
Dorian shows some of the ugliness growing in his own character, now that he is secure from aging, in how he reacts to Mr. Isaacs. He calls the manager a "fat Jew" and notes he is smiling very broadly. Dorian describes this as an "oily tremulous" smile. He is annoyed as well because the manager talks very loudly and waves around his "fat jeweled" hands. To Dorian, the manager behaves with "pompous humility." This perception contrasts to Lord Henry's, who says that he "rather" likes the manager, though Dorian wants to believe Lord Henry is being insincere.
In an allusion to Shakespeare's play The Tempest, Dorian thinks that he had come looking for Miranda, the beautiful daughter in the play (who would be Sibyl in the novel) and found Caliban instead. Caliban is the "monster" native to the island where Miranda and her father have crashed.
Dorian is becoming increasingly callous and judgmental.