Whose heart did the narrator actually hear?
The conventional answer, I suppose, is that when the narrator speaks with the police and hears the muffled noise, it is his own heart beating, but that isn't the only defensible answer.
The narrator advises us at the outset that he is "dreadfully nervous," but "the disease had sharpened [his] senses--not destroyed--not dulled them," and "above all was the sense of hearing acute." The fact that he says he even "heard many things in hell" should convince us of the extent of his madness. At the same time, we should never forget that this is a fictional story, where all things are possible.
Consider: just how possible is it to open a door slower than "a watch's minute hand," particularly when overcome with the terror and excitement the narrator speaks of? It is, however, possible in the narrator's mind and/or the fictional world he creates, which means that it is possible that he heard the old man's heart beating from the depths of hell itself.