Right, so I've noticed this happening myself for some time now, but admittedly haven't bothered looking into it until seeing you bring it up. I don't have much time this morning, but here's what I've found from the little bit of labbing I've done (if anyone discovers I'm wrong with any of this, feel free to correct):
Direction doesn't matter; it works going left and right.
Pound input angle doesn't matter; it happens with downward, normal, and upward pounds.
It happens on multiple stages (tested both Battlefield and Final D).
It can happen on platforms.
Air momentum doesn't matter; it happened at times with no momentum outside of pound's natural movement, with backward momentum, and also full forward momentum.
It happened out of FHs, SHs, and as your video displayed, falling from greater heights.
Using Jigglypuff's little forward flip animation after SHing as a guide, it appeared to happen most often shortly before Jigglypuff was completely upside down.
Similarly, a silent landing pound (normal pound with absolutely no sound effect) happened very often at around the same point. In fact, this happened more often than the no-momentum pound.
I'm going to guess Jigglypuff has to be at a very specific distance from the stage/platform for this to happen, and I couldn't find any evidence of consistency (at least not yet, even with 1/2 and 1/4 speed), so... I guess it's at least useful to realize the possibility of this happening if it's something that could mess with a player's planned execution.
I didn't get to test with FFing, slopes, reverse pound, or while hitting an opponent/object.
Hope this helps to answer some questions.
