Most converters will allow you to check the output voltage without being connected to a battery.
13.2 ->14.5 V would be a good range for a converter but I don't know what you have.
You also need to know how much current is being output to the battery and for how long. If you have an old power supply type converter, those that are a single stage, I would suggest getting a newer four stage converter.
About the explosive failure: Did the top of the battery's case stay intact but the sides exploded and fragmented? Just curious.