From the perspective of the old man, he is simply asleep until he hears the narrator's thumb slip on the "tin fastening" of his lantern, making a small, metallic, click. Such a sound would probably be terrifying because nothing natural, nothing that should be in the old man's room at night, could make that sound. He groans, a sound the narrator interprets as a result of the old man's "mortal terror," and the poor old man must be terribly frightened because he has not lain back down in bed. He's been sitting up, awake and likely straining to listen, blinded by his cataracts (probably the reason his eye seems "veiled") and the night. If he is that suspicious of the sound, it must be because he has some suspicions that the narrator is not quite right. If he thinks there's a chance that the narrator wants to kill him, it seems much more likely that he would remain awake and upright; if he weren't at all concerned, then he probably would have fallen back to sleep by now.
As alert as the old man is, the narrator seems even more alert. His mind is racing as he considers how the old man must feel as well as how he, himself, feels when he lies awake at night, the victim of "terrors that distracted [him]." He hears his own heart beat faster and faster, incorrectly interpreting it as the sound of the old man's heart, and so we get the sense that his adrenaline is racing faster and faster as the "beating grew louder, louder!"