It's interesting, I have the same ability: waking up 2-5 minutes before the alarm clock, feeling the washing machine or the oven alarm will ring in 20 seconds~2 minutes. I am rarely off and when I am it's by a huge margin. But I have no background or job or hobby history that would have helped fine tuned that. I also don't rely on it, I often set timers.
Eventually I was quite accurate on the current time, rarely missing by more than a minute, but at some point it felt like it wasn't really helping me since I had the watch anyway. It also was too weird for becoming a party trick (first time I admit to learning this), and didn't help with the idea that I had just wasted X minutes of my life between any 2 moments I thought about time or checked it without having done something useful, so I ended up disabling that.
I'm fairly certain that, at least in my case, it was a form of hypervigilance and based in anxiety. I'm less anxious these days and hope to live longer as a result.
Although I do still have a better-than-average ability to know when to check what's in the oven for doneness. This "feels" much different, though - I'm completely unaware of the passage of time until something just says to me "that stuff should be about done now."
The saying when I was in was "If you're not five minutes early, you're late." Which I understand they have optimized to everyone showing up fifteen minutes early now. Such a time-waste.
I always figured it went back to what you mentioned, being able to be on timelines down to the second while doing all the other ancillary tasks like listening to three radios, monitoring sensors, etc.