13S NMC does work on most 48 volt systems. You just need to dial in the correct voltages. What settings does the charging mode allow you to set?
My cells are NMC, but I am running 14S.
For daily cycling, I am charging to just under 4.1 volts per cell 57.2 volts / 14 = 4.0857 x 13 cells would be 53.1 volts. That seems to be about 88% charged. On the low side, I only run down to 51 volts each night before it goes back to grid power. 51 / 14 = 3.6428 volts per cell. x 13 = 47.357 for your pack to end at about the same discharge. My BMS seems to think that is about 60% remaining. I just took a snap shot of the BMS, it is still running at 51.42 volts and the BMS says I still have 67% remaining. It has only used 118 amp hours out of my 360. That is running about 6.4 KWHs out of the battery. I have not run a full capacity test yet, and since I am not running it up to full, it is very likely the 360 amp hour stated capacity is a bit high so it is over estimating what I have left by a bit. I should probably lower that entry to 320 AH instead of 360 AH to account for only charging to 88% or so. When I did have a real power failure, I did allow it to run on battery down to 22% remaining in the BMS. At that point, the battery was reporting 49.8 volts. That was still 3.55 volts per cell. Below 50%, the voltage actually curve and becomes much flatter. Still not as flat as LFP, but very noticeable on the voltage graphs. Both charging and discharging. 3.55 per cell x 13 = 46.15 volts on your 13S pack. Most of the power from NMC cells seems to come from 3.5 to 4.1 volts per cell. I can't predict the cycle life yet, but I am hoping to get 5 years out of my pack. That would mean 1,800 partial cycles from 50 to 90% charge at less than 0.3C charge and discharge rates. So far, I have cycled 1.3 Mega watt hours in and back out of the battery pack in just over 6 months (half a year).
For charging NMC cells, you should run 2 stage, no float charge. CC current up to 0.5C rate is good. Your spec page says the cells could take 1C, but that is hard on the cells. The spec sheet says the standard rate is only 0.2C so for 120 AH cells, that is just 24 amps, with 0.5C being 60 amps as the max I would run. My pack is 360 AH, and I have not yet exceeded an 80 amp charge rate, or just 0.222C rate. At this slow rate, my cells use 5-6 hours while the sun is up to charge fully. So Bulk charge at CC of no more than 60 amps (20-24 is better) up to the absorption voltage which should be 4.1 volts per cell or 53.3 volts for your 13S pack. Then absorb charge at constant voltage of 53.3 until the current falls under 0.02C at which point you are full at about 90% charged. No float current. Don't run the inverter down lower than 3.0 volts per cell. 39.0 volts, is probably lower than the inverter will run anyways. My 14S cut off at 42 volts minimum during a grid power outage. When my grid is up, I leave the cells above 3.6 volts, or 46.8 volts on your 13S pack. You can certainly run lower than that, but I am holding a reserve for over night grid failure. The harder you charge and discharge, and the beeper each cycle goes, the less cycles the battery will give you.