The Doctor said that he had to stay relative to the Master within the causal time nexus. Timothy Dalton's Timelords intentionally broke this causal nexus rule to retroactively make the Master hear the sound of drums. From the Timelord's perspective, the universe and time is going to end anyway, so such an infraction can be ignored.
Just like Star Trek, the timeline has diverged and this is an alternate universe/timeline. The original Master, his backstory and such are still intact in the original timeline. .
This is basically it - Delgado and Ainley etc weren't hearing the drums when you watched them, cos the Timey's hadn't caused it yet. But next time you watch them, they will be.
Of course, the signal probably gets stronger as it nears Simm, and so it probably isn't driving Delgado nuts - hell, he probably just notes that he's hearing his own heartbeat...
I think that's probably the best way to think of it. Simm did say the drums were getting louder in Last of the Timelords.