Stephen,
What you have there is 3 x 12v sealed lead acid batteries (SLA's) - yes, this is a typical arrangement. Judging by the specifications and the lights on the front panel, the charger looks to be a "smart" charger - ie one that is designed to detect when the batteries are fully charged and then switch into a maintenance mode.
However, as I can't read the Chinese characters, I'm not certain of this. I assume when you first connect the charger after a ride, one or both of the green lights are unlit. They then light up when the battery is fully charged.
If it were my bike, I would follow the advice in this article -
http://www.steveduncan.net/html/caring_for_slas.htmlIf you have to use a questionable charger, disconnect it after the charge cycle is complete. Learn what an appropriate “finishing” voltage is for your brand of SLAs and then see what your charger is really doing.
Tip #3: Charge before and after every ride.
Topping off your SLAs before a ride will give you the longest ride and maximum initial power. Charging immediately after a ride will prevent sulfation of the plates from starting to occur. You may wish to let your batteries cool before charging, just to be nice.
So I would disconnect the charger after a full charge is reached and then recharge again before I went for a ride. Or If the bike isn't used for a while, I would give the batteries a charge every few weeks.
Hope that helps.