OK. I don't really understand what you're saying.
The charging profile for Li-ion is pretty standard (**broken link removed**). The BMS has over voltage, under under votage, short protection etc. Can you explain what you mean, technically, about a proper charging unit? Surely if the BMS is managing and balancing the voltage/current the input type is irrelevant? That is, if the PSU can mange the correct power the BMS should regulate/balance and cutoff the charge to the cells as required?