[Mr V]

I'm sorry but that charger is illegal to use and will degrade battery life. The max recommended charging amperage of the FRC legal batteries is ~6 amps. Charging at a higher rate can cause overheating and over time damage to the battery.

That charger is intended to be used with an automotive sized battery not a FRC legal sized battery. It says that it "automatically" selects the charge rate but that is misleading. The battery is what sets the charge rate based on its voltage. Since the charger "thinks" that it is connected to a much larger battery it will charge at too high of a rate.

The reason you are seeing different voltages when you disconnect the charger is caused by a couple of factors. One is the state of charge when the battery is connected. That will set the charge voltage and rate. The other is the phenomenon known as a surface charge where you are seeing a little residual voltage on the surface of the plates. To test the batteries voltage you need to either let is sit for a number of hours, which is preferred, or remove the surface charge by connecting a light load to it for a couple of minutes. The max voltage of a fully charged lead acid battery that has had its surface charge removed or allowed to "soak" in is 12.77 volts.