The Custer referred to in the story is General George Armstrong Custer whose battallion was exterminated by a coalition of Native Americans in the battle of Little Bighorn in 1876. Custer himself died in the battle, which is also known as Custer's Last Stand. This controversial historical character recurs throughout Alexie's literary production and not only in The Lone Ranger and Tonto Fistfight in Heaven. There is, for example, an interesting poem called "Custer Speaks" which you can read alongside the reference in this story and in "All I want to do is dance".
In "Distances", Custer is charged with having caused a new apocalypse on the earth which, paradoxically, is affecting more whites than the Indians. To understand that, one should go back to Custer's controversial behavior (particularly during the Bighorn battle) and personality. To Alexie, Custer represents the worst of white brutality and individualism. In the Bighorn battle, Custer went against the orders he had received to capture Crazy Horse and, in doing so, he caused the deaths of hundreds of his men. Because of his craving for victory and fame, Custer went against his own people. That's the reason why the narrator in "Distances" holds him responsible for such an apparently perverse act against whites.