Do I understand correctly that the 'balancing act' works by discharging the cell(s) with the highest voltage and equalizing the cells that way? Looking at the schematic I don't see how it could charge individual cells this way.
That's my understanding, and yes the cells are charged in series.
Since the maximum discharge current (1A?) is less then the max charge current (6A depending upon the attached power supply), I guess the cycle is:
Charge on, discharge off
Wait until at least 1 cell is is fully charged
Charge off, discharge on
Wait until all fully charged cells <= highest voltage of uncharged cells
... repeat until all balanced and charged?
Balanced charge is just one option. Quick charge ignores the individual cell voltages (?).
I thought the really neat thing about this charger was the ability to calibrate it to within 10mV. Then I bought one, then I bought a Solartron 7150+ and discovered the charger was only 10mV over straight out the box

YMMV of course.