Here I sit, at my laptop, looking at the clock, not yet 03:00 and I know that I'm probably up for the day? How do I know? I've a simple barometer of whether I'm done sleeping for my stretch. If I wake up, and I hear music, I know my brain has woken up and likely won't go back to sleep - at least, not easily and probably not for long.
Since I need to get up before 06:00, today, attempting to sleep till my alarm would likely result in less than two hours additional sleep. Probably not worth the effort. Probably not worth the anxiety of sitting there, watching my alarm clock click onwards towards my target waking-time, wondering "can I actually get back to sleep for a meaningful ammount of time."
The funny thing with my internal wakeup music is that, as much as I can tell by it's presence that "I'm up", I can also frequently tell how "up" I am. If the music is strong, loud and relatively complete, there's no point even trying to go back to sleep. If the music is just barely there, especially if whatever my inner-DJ's playing is at a low volume or is just a line or two of whatever music is coursing through my head, I know there's a chance that I might get back to sleep. I just have to wait it out and hope the music fades or comes to a stop.