I have a Schumacher microprocessor controlled "intellicharger" or some other marketing nonsense charger.
First off, the battery % number is worthless. Do not even press that button to look at it.
Mine also will go up into the high 16's. Sometimes It will shoot up to the 18's and shut itself off. This can be dangerous for some electronics if it is still hooked to the vehicle, though I have not had any issues yet. Usually it will do this only when I put it on the 12 or 25 amp setting, and the batteries are within 20% of fully charged.
I sometimes use the AGM settings on my flooded batteries as it is less likely to go upto these extreme voltages. The biggest difference in the AGM setting is the float voltage. It is higher on the AGM setting. I have a digital amp hour counter/ battery monitor, so I get to see how much amperage the charger is putting out throughout the charge cycle.
Basically as the battery gets closer to fully charged, the volts rise and the amps taper downward. When the battery is accepting less than 5 amps, the charger might decide to go into float mode, but sometimes I see mine continue upto 15.5 volts and still be pumping 10 amps into my batteries. I only allow this for about 20 minutes twice a month at most, as these equalization voltages can cause excessive plate shedding. Especially at 10+ amps. It is just way too much for 2 group 27 batteries, which are pretty large batteries at 115 amp hours each.
Basically, my Charger is a POS, and I cannot trust it to not overcharge my batteries. It is neither smart or automatic, and If I had not hardwired it to my deep cycle battery bank, would have returned it. I use it regularly, but I do not leave it unattended. Sometimes it works perfectly, and goes into float mode right when my amp hour counter says the batteries are 0 amp hours from full. Other times it just keeps going well past it, sometimes it goes into float mode well before the batteries are full. There is no logic to it that I have found in it's 3.5 years of use. It does what it wants with no rhyme or reason, the batteries are just along for the ride.