[Azura]

I'm not sure what is going on but the in-game clock usually desynchronizes when you speed up the demo. For example, you could get a count-down even though the end of match is still moments away. What you could try is speeding up the demo and then bringing it back to normal speed for a while.

As for curtime, think of it as the relative time within the demo (it's a demo manager specific command). It has the advantage of remaining precise whatever you do which makes it suitable for movie-making purposes. It's what I'm using for my movie.