A reformatory is like a reform school or a detention center for youths. This "young man" is a white guy who works at the reform school where Absalom was placed after first getting into trouble with the law.
Have you guys ever heard the term "self-insert"? It's when an author creates a really obvious avatar, a clear stand-in for the author herself, and sticks it into an otherwise fictional universe. So, if you come across a fan story in which a perfectly ordinary American high school girl suddenly appears in Middle Earth to join the quest to kill Smaug along with Bilbo Baggins and Thorin Oakenshield, that's probably an example of self-insertion.
We want to emphasize that self-insertion isn't necessarily a bad thing—we all like to dream about hanging out with our favorite fictional friends. Really great professional writers like J.K. Rowling have admitted that some of their characters closely resemble them in real life (specifically, Rowling claims that Hermione is "a caricature of what [she] was like when [she] was eleven" [source]).
Still, self-insertion can be a bit transparent and obvious as a narrative device: if there is a character who is supposedly ordinary, but who nonetheless receives a ton of attention from the fictional people around her, this "character" may actually be a substitute for the real-life author indulging in some wish-fulfillment.
All of this is to say that the young man from the reform school—nameless, but he appears several times at important plot points to do with Absalom—is a clear self-insertion of Alan Paton into Cry, the Beloved Country.
In our "In a Nutshell" section, we mentioned that Paton put in some time as the administrator of a reform school for black youths called Diepkloof. Paton's whole idea was that these youth centers should be more like schools than like prisons. Like the reformatory in Cry, the Beloved Country, Paton's real-life reform school also gave kids with a history of good behavior the chance to live and work in separate housing off the school grounds (source, Introduction). It's because of this actual policy at Paton's school that fictional Absalom gets to live away from the reformatory in the novel: "partly because of his good behaviour, partly because of his age, but mainly because there was a girl who was pregnant" (1.10.66).
In fact, one of the inspirations for this whole novel may have been an incident that happened at Diepkloof while Paton was in charge there. One of these youths who were allowed to live independent lives off the school grounds thanks to their good behavior actually did break into the home of a white family. Like Absalom, this youth accidentally shot and killed a white person—a woman—who surprised him while he was committing this burglary (source, Introduction). So clearly, Paton is writing about something he experienced directly: the criminal justice system in South Africa as it related to black youths in the 1940s.
Paton's form of self-insertion in Cry, the Beloved Country is very mild. He definitely isn't the hero of the book, and he doesn't attract a lot of attention from the other characters in the novel. This isn't a piece of Harry Potter fan fiction where an American exchange student mysteriously turns up to take all of Hogwarts by storm (a classic self-insertion cliché). However, when Paton's nameless character expresses frustration at Absalom for his irresponsibility in leaving his job and abandoning his pregnant girlfriend, we get the sense that it's real-life Paton expressing his own anger and concern at the kids he knew at Diepkloof, who may not have always made great choices with their lives.