The song doesn't run at the same speed in both levels, also it isn't time that's physically moving faster, it's only the dreamers' perception of time.
The song isn't running any slower, and is operating outside the dreamer's sphere of influence. The fact that the song should be played at the same speed is the very metronome like constant the dreamers are depending upon to synchronize their kicks.
However, the dreamscape seems to evade such rules...
During the third 'Layer' of dreaming, the cue that the dreamers hear isn't a song, it's just a very loud, very low note followed by what appears to be a fractured echo. This could be a particular note from "Non, Je ne regrette rien", the Edith Piaf song that is used as their kick.
Whilst it's old news now, I was incredibly impressed to discover that this slowing down or 'condensing' of music was reflected not only diegetically (hence the almost foghorn sounding note in the third layer), but also in the soundtrack.
The Inception theme music, famous (and often parodied) for its swelling section, is mixed brilliantly into a slowed down version of Piaf's song itself; in order to replicate the expansion of the music, the very thing you are discussing.
It's maybe difficult to understand in writing, but helpfully someone has already made a video comparison to explain things better.
Interestingly, one commentator has made reference to the fact that the Piaf song is 2 minutes 22 seconds, and Inception is 2 hours 22 minutes. Coincidence? Unlikely.