The confusion arises from the fact that Poe's original burial was relatively simple and private, attended by only a few friends and family. He was buried in a "common grave" in Westminster Burying Ground in Baltimore.
Later, a group of Poe enthusiasts and admirers, realizing the literary significance of his work, decided to honor him with a more fitting memorial. They raised funds and organized a more public reburial, moving his body to a designated plot in the same cemetery. This event, which occurred years after his initial burial, is what is often misconstrued as a "redoing" of the funeral.
In essence, Poe's original funeral was a simple one, and his later re-interment was a public ceremony to commemorate his literary legacy, not a repeat of his original burial.