Your manual is pointing out, that if you downshift at too high an RPM, that RPM will increase after you come out of the shift. So if you are at 5000, and you downshift, you’ll be coming out of the shift at around 8,500. And that’s just fine if your redline is at 14,500. However, I think your over-cautious manual is trying to point out that if you downshift at, let’s say 10,000…that sucker is going to jump to near redline, and it’s going to be a bitch and you might lose it.
When you downshift, you are going to a lower gear. Lower gears accelerate much faster than higher gears (depending on where you are in the RPM range). So if you are cruising along and require instant acceleration, you will downshift, throttle up, and then shift back up after you are at the speed desired. That is what they mean by downshifting to speed up. Slow accelerations are still possible by throttling in the gear you are already in…but why wait?!
Let off the throttle for the split second when you switch gears, don’t gas it. Letting the clutch out slowly will be your biggest ally in learning how to shift. Learning where the gears start to catch is something even experienced riders have to do when they get on a bike they’ve never been on before. Once you get the concept down, you’ll get much more efficient at it. PLP is key here. Dealing with everything that comes with driving on the street ON TOP OF learning how to shift is going to be too much for you to focus on.