Yes it regulates the negative cycle, with the battery being used as a clamp for the positive cycle, and the SCR1 side dropping charge current for the battery when it reaches 14V4 to a lower value, and then SCR2 is there to clamp the negative side, shorting out the coil, as that will limit current due to the core saturating hard as the current rises, limiting the current flowing in it. Not the best, but has an advantage in being cheap and easy to implement, plus they do not need to have a charger in for the versions with pull start, simply have the lamps on all the time, and put in the AC regulator, which is basically SCR2 side wrapped with a bridge rectifier, to do the same. You can replace with a lot of universal regulator units as well, some are better, some are worse, but all operate on the same rough principles.
Most common faults are the diodes and SCR units cracking from the thermal cycling, and going intermittently open circuit, which as you found means high AC voltage on a half cycle, depending on the diode or SCR that breaks. Normally the generator is the same number of poles as the number of cylinders, times 2, simply because the generator uses the same magnets as the ignition circuit, so for a single cylinder 2 stroke it is 2 pole, for a 2 piston 4 pole, as they normally are wound on the same rotor as the ignition system.