Someone didn't pay attention to the episode.
It is explicitly stated that the drumming was retroactively implanted in the Master as a child.
Could well be that I didn't pay attention well enough. The way I understood it, the retroactive implantation meant that the Master
thought he had heard the drumming since he had been a child, but it really only existed in his current incarnation, which was the Time Lords' way of extracting themselves from the time lock to modern-day Earth.
None of it really makes sense, and either interpretation is valid. I just think that between the Time Lords resurrecting the Master during the Time War (as said in "The Sound of Drums") and the drumming sounds hitting Simm's Master and
only that Master), it works better in my mind that the Time Lords saw the current-day Earth, retroactively implanted the drumming into the Master's mind so as to drive him mad and then hurled down the diamond so as to embrace the current Master's insanity.