We all have an anecdote or two about real-life sensations—the smell of cooking food, the noise of thunderstorms, or the pressure of a full bladder—that made appearances in our dreams. It’s not even that rare for external stimuli, when they happen to occur during dream-producing REM sleep, to be incorporated into dream content. A number of experimenters have asked participants to fall asleep in the laboratory while playing audio recordings of names, zapping them with mild shocks or wafting the smell of lemons under the sleepers’ noses. Upon waking, participants reported incorporating these sensations into their dreams anywhere from ~10-80% of the time, depending on the study and the type of sensation (see here or here). Surely this is what happened to you and your cat.
But you say that the cat started hammering on you only after the drumbeats began sounding in your dream. Shredl et al. (2009) found that rather than the dream becoming explicitly about the sensation, the stimuli were often incorporated indirectly: for example, rose scents instigated happy dreams, while the smell of rotten eggs led to unhappy ones. So my guess is that the tapping was simply incorporated into the dream in an indirect way before you began to wake up and become aware of the presence of an impatient feline on your chest.
The other possibility, of course, is that your cat is able to read your mind. More far-fetched, however, is the supposition that a cat could be interested in the content of its owners dreams.
Effects of Somatosensory Stimulation on Dream Content, Koulack, 1969