Related to this question and TMN's answer: What's a good RPM range to safely downshift an automanual transmission manually? My car does it for me when the RPMs get really low, but that throws me off at times and I'd like to beat my car to it sometimes. If I downshift a too high RPMs, I get a slight jerk forward, I've never driven a stick but I'd imagine it doesn't happen since the clutch is supposed to be disengaged when braking.
If your RPM shoots up when you downshift it should cause your engine brake to or slow down. (Unless you still have your foot on the gas). I would say TMN was probably thinking about over revving the engine when downshifting If you are at 4000RPM in 4th then you downshift to 3rd and your RPM goes up to 6000+ or anywhere close to the redline you could potentially do damage to the valves in your engine.
That doesn't take into account what your transmission is going through when you do this. I would say you don't want to downshift and cause your engine to go over 4000RPM. I used to do this with my automatic as well and I tried to find the downshift points which would leave my engine at around 3200rpm. This gave a decent amount of engine braking without jerkiness or engine noise.
That being said the safest way is to just let the auto control the downshifts. Doing this could theoretically wear out clutch packs sooner so you may want to change your trans fluid more often.
In a manual the clutch doesn't have to be disengaged while braking in fact you will get better efficiency if you leave the clutch engaged while braking until you are just about to stop (or stall).