Ok, I think you've got one crucial thing backwards. A "system" is refered by it's nominal system voltage of the battery bank.
The whole definition of "12v panel" or "24v panel" comes from marketing where a "12v panel" can provide enough voltage on its own to charge a "12v system" but not enough on its own to charge a "24v or 48v system". The 12v panels will often put out 18ish volts at full bore, the 24v panels can do 30ish. Now, you could put 2 of the "12v" panels in series to feed a 24v battery via PWM, but by the time you're getting into a system that big you're already into the range where an MPPT controller is worth the expense.
In the world of charge controllers you've got your basic PWM and your smarter MPPT controllers. In basic terms, a PWM controller lets as much voltage through as the battery can take and just clips the rest off as waste. If you've got 18v of panel trying to pump 14v into your battery, that's 4v just being clipped off. If you were to put one of the 30v panels on the same battery, it would clip 16v off as waste which is a huge waste of panel. Up to about 3-400w of panels on a 12v system, a PWM will work fine. Larger than that and a MPPT starts to be a good investment.
So, to get around this we have MPPT controllers that take the incoming higher voltage and transform that into lower voltage but higher amperage out to the batteries. Much more efficient use of the panel.
Once you start stringing multiple panels together in series that voltage gets really high which is good for running long wires, but can't be used directly to the battery.
So, that 4210 you've got is good for 40a of current to your battery, and up to 100v of incoming voltage, or VoC. It can only work at 12v or 24v nominal battery voltage, so there's no getting these to feed a 48v battery system. But, that means you can use 40a × 12v =480 watts of panel. The hard, and I mean DO-NOT-CROSS-THIS-LINE thing to pay attention to is the VoC of the panels and the MaxPV Input of the charge controller. Solar panels create more voltage when cold so 80% is a good number to aim for, or about 80v VoC in your case. Your 3 panels are 70v so still a healthy voltage.
Did that make sense?