"servile black man," 1922, somewhat inaccurately in reference to the humble, pious, but strong-willed main character in Harriet Beecher Stowe's novel, "Uncle Tom's Cabin" (1852). The image implied in the insult perhaps is more traceable to the late 19c. minstel show versions of the story, which reached a far wider audience than the book.
I don't recall anyone in the 1920s using the term 'Uncle Tom' as an epithet. But what's amazing is how fast it caught on (in the 1930s). Black scholars picked up (the term) and just started throwing it at each other. [Ernest Allen, quoted in Hamilton, Kendra, "The Strange Career of Uncle Tom," Black Issues in Higher Education, June 2002]
As a verb, attested from 1937.