I just spent a couple of hours trying to figure the same thing out. I finally found a clue: https://youtu.be/sbNRaqrar7g?t=160
The link to the cheap ebay BMS you sent is now broken but I guess it was like many of the cheap one that use a HY2120 series chip, emphasis on series. When I looked at the chip on the 2S 3Amp BMS I have under a microscope it had "2120 CB" written on it. If you look at the datasheet for the HY2120, on page 6 you see that different variations of the 2120 chip have different overdischarge detection and release voltages, from 2.25 up to 3.2 with the CB one I have at "2.90±0.08V". I suspect this is where the range of voltages in the descriptions of cheap BMS's comes from and it is really only one value depending on which specific 2120 chip is on the board being sold. I was also wondering if it (re: data sheet page 6) could refer to the "Overdischarge detection voltage" vs. the "Overdischarge release voltage" since that yields a voltage range but I'm not sure that would make as much sense...for the 2120 CB BMS I have those values are 2.9V and 3.0V from the data sheet but the product description on Aliexpress for my board still "Over discharge voltage: 2.3-3.0v±0.05v" which makes me think it's more what I described above since 2.3V isn't shown on the data sheet for the 2120 CB.
As a minor side note since it was hard to find this info: the reason for investigating this was trying to understand if this Li-ion BMS would work for LiPo. Discharge to 2.3V would have certainly killed a LiPo, discharge to 2.9V seems to be debated but at least one person suggests 2.9V is ok.