Why does the output of a transformer increase when connected to a battery for charging?
If you are measuring full wave rectified DC with a meter, and see 13.8v average (average is what a DC meter reads), then the peak will be rather larger, on the order of 20v. This is what is causing an excessive current to flow into the battery. As the battery is fissing, its terminal voltage rises above what's safe, to give you the 15.8v you read on the meter.