The drum beating in "The Emperor Jones" is an indication that the natives are preparing to attack the Emperor. They beat the drum and perform a war dance to get into the right frame of mind to kill the Emperor.
As the natives perform their ritual ceremony, the beating of the drum begins to take on a symbolic meaning. The drum beats appear to mimic a human heart beat, that of Emperor Jones.
"Fatigued from his afternoon hike in the hot sun, Jones rests, listening to the steady beat of the drum, pulsating at a little more than 72 beats a minute, the rate of the normal heart beat."
As Jones, begins to become more exhausted and frightened, he hallucinates all types of images. The drum beats follow his rising and falling fear, the sound alone terrifies him, it puts a spell on him.
Therefore, you could say that as a form of black magic the drum beats appear to be chasing Jones, and responding to his anxiety. It is as if the natives who declared war on him with their dance are spiritually hunting him through the sound of the drum beats, killing him without ever touching him. When the drum beat catches him, it overtakes him, killing him, the drum beats stop, so does the Emperor's heart beat.