Sure it is faster, but the trigger to make it happen seems 100% random.

I've had it happen twice now, and I have no idea what I did to get it to happen. I "try" for it every time I start a run, but have never found anything that works.

The movement slowdown is triggered by the geometry pretty much. Not by Jack at all, and him appearing has no relation to the actual slowdown. You can tell this because if you walk back over that particular patch of land over and over, it will always lower your movement speed.

Similar to how in some games where water will slow your movement speed, when it's actually just particular pieces of geometry being programmed to lower your movement speed / animations by a certain %.