Yeah, I'm pretty much sure OP is unnecessarily complicating things. It I am getting up like 5 minutes before the alarm every time I know I really need to get up at that specific time (because I know something more important than just dragging my ass to the fucking office needs to happen this time), well, that means I somehow know subconsciously really well what's the time is. Because either I'm living in my sleep ever since, or I actually got up, turned off the alarm clock so it won't bother me, got dressed and went on with my day. Not just lied there fooling myself I'm awake before I actually got awake.
But even if your brain is measuring time operating at a precision of "around five minutes before," the variance will sometimes cause that to be 3 seconds before.