The phrase “long after midnight” is a key one in Bradbury’s work. Many of his stories (or at least key events in them) take place “long after midnight.”
In 1950 Bradbury used the phrase as the working title for a 140-page manuscript that was the predecessor of Fahrenheit 451, a 1984-like nightmare in which Montag was "caught and reported by a young boy for reading books," according to Ray Bradbury: The Life of Fiction by Jonathan R. Eller and William F. Touponce.
The title passed on to other tales, including a short story written shortly after Something Wicked, though it was not published in book form until 1976 (as the title story of the collection).
Here, of course, it refers directly to the time when the carnival train arrived in town several nights before, but also note Mr. Halloway’s long paragraph of thoughts in chapter 14 concerning that “special hour” of 3 a.m.