Motorcycle & Scooter

From what you are saying I'm initially thinking it's the battery hence the engine speed difference when you disconnect the jumper cables. The battery, stator, and rectifier all work in tandem. If the battery has a poor charge or is dying the voltage will be off. The rectifier will having difficulty in balancing voltage to charge the battery as the engine runs, and the stator voltage will all so be off so the output to run the engine can drop hence the rough idle and revving. When you connect the jumper cables back, the battery that is providing the charge is taking over to balance the voltage and everything smooths out.

I'd recommend first replacing the battery. It should cost around $75 or $80.
If that does not work, then I'd go with a rectifier. For your bike that would be about $110.
Worst case scenario is the stator, which will run about $125.

The easiest way to test this theory is to disconnect your battery, and connect (carefully) the battery leads to the battery/vehicle you jumped with. Make sure that vehicle is not running. If the bike runs fine, most likely its just your battery.

Good luck.