I have a similar cheap PWM controller. It turns on and off varying the on percentage, modulating the pulse width. Actually it isn't that fancy. When the voltage goes above the set voltage, it goes off. When the voltage drops below the set voltage it turns on. The micro computer checks the voltage periodically. The display shows the last measurement. An on period can make the voltage higher by several tenths of a volt making it appear unstable. You can use a different meter at the battery. If you have a long skinny wire from the controller to the battery, use another meter at the battery.
My controller has one charge voltage setting. The instructions call it "float" but I call it "the" voltage. Above, its off, below it's on. If the battery is substantially discharged it stays on for a long time. Some people call that bulk. I keep mine set to 14.4 volts in the summer and 14.8 in the winter. I have a flooded battery not a sealed battery so I can add water. A sealed AGM battery should be charged at 14.4 to 14.8 until the charge current drops to 1% of the capacity rating so 1 amp for a 100 amp hour battery. The decreasing current is a function of the battery. The charge controller maintains a constant voltage.
Your controller is probably set to 13.8 volts. If the battery is substantially discharged it will slowly rise to the set voltage then stay there.
Fancy controllers will go to 14.4 volts then go to 13.8 when the battery is full. The problem is how do they decide the battery is full? They don't have a hydrometer to check the acid. If they measure the charging current how do they differentiate between the diminishing current going to the battery and current going to the fridge? With a shunt resistor they could measure that. Some measure all current into and out of the battery and keep score. For those to work they need to know the actual battery capacity, not what it was when new. It all gets very complicated.
Do you have a sealed battery or a flooded battery? When you got the second kit with a second battery did you connect the two batteries in parallel or did you just keep the systems separated?
Presume that the original charge controller setting is not right. If you bought a new car it would come with the windshield wiper set to off. That might not be the correct setting particularly if it starts to rain. In Arizona off is probably correct all the time. Observe what your charge controller does. What settings are there? What do they actually do?
For testing you need to have known discharging of the battery. I use old headlight bulbs. The low beam is burned out but the high beam is a good load. Measure the current. Battery capacity is at the 20 hour rate. A 5 amp load is right for a 100 amp hour battery. If you take out 5 amp hours the controller needs to put back that much plus 20%. 13.8 volts isn't the right answer, 6 amp hours is.
