I discovered this too recently.
Own a Husqvarna battery pack that died and found two of the 20 cells to be dead, so took an interest in lithium ion batteries and charging. Bought a cheap multiple cell board for what I thought to be for balanced charging and protection, to indeed discover that it does not have a balancing function. So yes it cuts off when one of the cells reaches the set over protection voltage.
The used IC is capable of balancing, but needs an additional mosfet and discharge resistor per cell. This method is not the same as active per cell charging, and I'm not sure that this even exists in a standard IC setup.
In balancing mode it will discharge cells that are to high and then continue normal charging, and rinse and repeat this cycle until all cells are at the same charged level. Thus wasting energy.
To get my Husqvarna battery pack working again I had to manually equal the cells with a separate power supply because the official charger would fall back into error mode every time it detected the unbalance.