If I had to choose one word for this story, it would be "subtle." I know that that sounds overly melodramatic, but what I mean is that I'm impressed about the subtle way that Waldrop has decided to deal with time travel in this story. He shows the consequences of going back in time to change the past, and, as a result, the present, but not in an overblown "Oh No, the Nazis won World War II! And then the Commies took over!! And I'm my own grandfather!!!" kind of way. The changes that are wrought in Waldrop's story are small, and the consequences equally so. Of course, they have significant repercussions for the story's protagonist, but not necessarily devastating ones.
Because these consequences are so small, Waldrop ends up focussing much more of his time on the life of his story's protagonist, Franklin (Bubba), and the protagonist’s sister Ethel than on the time-travel element. The reader receives lush descriptions of key scenes from Bubba's childhood, and you really get the feeling of what it must have been like to grow up in 1950s / 1960s Texas and Alabama.* In my mind, this is really the only way to make the reader care about the changes that are made in Bubba's life as a result of the time travel. Without the background, the changes, which are really only implied, would not make sense, and certainly wouldn’t have the same degree of impact.
In the end, I have to hand it to Waldrop for taking an overdone SF trope like time travel and, while not really doing anything new with it, still managing to create a compelling story. Actually, I think that the story itself could have been compelling without the SF elements at all. The story stands well on its own as a story about growing up in the American south in the middle of the 20th century, without having to complicate things with the time travel angle.
*Actually, I wonder how much of the story is based on Waldrop's and his sister own childhoods, since he dedicates the story to "Ms. Mary Ethel (Waldrop) Burton Falco Bray Hodnett, my little sister. . . "