Dill has not actually met his father. Dill likes to invent stories, and the story he tells about his father in Chapter 4 is merely a fabrication.
Early in the narrative of To Kill a Mockingbird, Dill establishes himself as a teller of tall tales. For instance, in Chapter 1, there is this exchange between Dill and Scout,
I asked Dill where his father was: "You ain't said anything about him."
"I haven't got one."
"Is he dead?"
"Then if he's not dead you've got one, haven't you?"
Then, in Chapter 4, Dill arrives from Meridian, Mississippi. He tells Jem and Scout that he ate dinner in the dining car, and
...he had seen two twins hitched together [conjoined] get off the train in Bay St. Louis and stuck to his story regardless of threats....and said he had seen his father. Dill's father was taller than ours, he had a black beard (pointed), and was president of the L & N Railroad.
This latest story contradicts what Dill has said in Chapter 1; in addition it accompanies Dill's obvious fabrication of the conjoined twins, so his credibility is destroyed before he says anything about his father. Of course, the pointed black beard also rings strange, too.
In other instances, Dill has boasted or exaggerated such as when he first met Scout and Jem, saying if they needed anything read, he could read it. Then, as more evidence that Dill is rather glib and has a penchant for making things up, on the night that he and Jem have tried to see into the Radley home, he smoothly and quickly tells Jem's father that they have been playing strip poker by the fishpond.