The fact that it is an MPPT controller isn't relevant to whether or not it will/can overcharge your batteries. MPPT only means that it will draw the most favourable amount of current from the panels and deliver this to the battery with as little losses as possible. But that doesn't mean it is "always" delivering max, it will only do that during the phases where it is safe to do so. But generally speaking I'd say that MPPT controllers are less likely to overcharge the batteries than other charge controllers, because they have more accurate and sophisticated electronics/control circuitry than cheaper PWM/linear controllers.
As with any battery charger or charge controller, it depends on the accuracy of the unit. With chinese ebay stuff you never know what you get. But if you have a decent MPPT controller from a reputable manufacturer it will handle it fine, and will normally have different charging profiles or manual settings that you can play around with. Either by selecting a specific chemistry, or by specifying all the parameters yourself.
I have a Victron SmartSolar MPPT controller, and it lets me set the overall max current that it will never exceed. For example if you have a small battery and your PV exceeds the current limit of the battery. It also slows the charge current depending on the state of the battery, or more specifically, depending on the charge phase it is in.
In my case I am using it with AGM batteries. a 48V battery bank (but for simplicity I'll divide by 4 for a 12V battery). Charging goes as follows:
1. The charge controller will first push as much current as it can into the battery, as long as the voltage is less than 14.40V (Bulk phase). This is where you benefit the most from the MPPT circuitry.
2. Once 14.40V is reached, it will reduce the current gradually, to maintain the battery at a constant/no more than 14.40V (Absorption phase). It's no longer tracking the peak point of the panel, rather it is keeping a constant voltage on the battery.
3. Once the current gets so low that the battery is no longer absorbing a charge while maintained at 14.40V, it drops the voltage to 13.80V and maintains that voltage to trickle charge the battery (float charge). If a load is attached to the battery, it will try to deliver the current needed to stay at 13.80V.
Every once in a while, it re-enters the absorption phase by ramping the voltage back up to 14.40V for a slight moment to see if the battery will accept more current, and top up any missing charge, then enter float state again.
This is for AGM batteries. Lithium batteries will have a different pattern, or different durations for each charging phase.
