I've read a lot of warnings from charger companies not to run their chargers with a auto type batt chargers. Look in the manual for ICE charger, warning is listed on page 3 - "Do not use automotive type charges to power the charger".
The power they supply is not 'clean' enough and can damage the charger. Get a proper power supply - you can find inexpensive ones from places like HobbyCity for cheap.