The first thing to ask is:
When you are regen braking and the battery is full, does the braking action cut off at all? If not, then for whatever reason the BMS is definitely not cutting off (whether it "should" or not might be another story, depending on design/hookup).
As for whether it will cut off current:
It depends on how the BMS works and is wired. Some BMS's charge thru a separate port (and FETs) than they discharge thru, and in that case there won't be any cutoff of regen charging currnet, because the discharge port the regen comes in thru probably only cuts off under cell or pack LVC conditions, not HVC.
If charge and discharge are thru the same port/FETs, then either HVC or LVC should cut off the FETs, so regen current should also be cut off.
However, if your BMS does not disconnect under cell-level HVC but only pack-level HVC (which some seem to do based on failures people have seen), then until the whole pack reaches HVC it wouldn't cut regen current off, and any already-high cells would then get overcharged.
If your BMS is supposed to do cell-level HVC and cells are indeed being overcharged by the regen, and it also uses the same port for charge and discharge, then it also could theoretically overcharge off the wall charger, too, if that charger was high enough voltage to force current thru the pack past it's normal cutoff, because it means the BMS is not working correctly.
I'd guess the last is the most likely problem--either a design flaw or a failure in the BMS itself.
It could also be that the FETs have failed, which since that's normally a short, would allow current to flow whether or not the BMS is trying to turn them off or not (meaning the rest of the BMS could be working properly, but the FETs can't turn off anymore).
That oculd happen from overheating, or from higher voltage across the FETs than they are rated for, or a number of other reasons.
You can test this a couple of ways.
One is by using an ohmmeter and measuring across the source and drain legs of the charge/discharge FETs, when you know the BMS should have cut off the current. If the reading is low ohms, then it's not working. Then disconnecting the BMS from the battery completely and remeasuring, and if the reading is STILL low ohms, then the FETs are probably shorted and will need to be replaced. remove the FETs and remeasure, and if it's now high ohms hten repalce with new FETs. If it's still Low ohms you have some other problem inside the BMS or PCB, or are measuring in the wrong places.
If the reading of the first measurement is high ohms then it *has* cut off the current. If the reading of hte second measurement is high ohms then the FETs are ok, but just not being told what to do correctly by the BMS when it's powered up. For that you can start measuring the gate of the FETs, relative ot battery negative, to see what they'r ebeing told to do and when.
Another is by monitoring the voltage on either side of the FETs (source ot drain or drain to source) during charging, as well as the cell voltages, and when the BMS is supposed to be shutting off during a cell or pack level HVC event, if the voltage is the same on either side of the FETs then it's not cutting off--if the voltage becomes different after the event than before, they are working. If not, they're either shorted or not bieng controlled ocrrectly by the BMS.