High School auto shop exam question was voltage per cell on a fully charged automotive lead acid battery. A: 2.2V.
Mutiply by 6 cells to get battery voltage
Higher voltages push current into the cells. So, your 13.8 will push current into the battery.
Your DC-DC is not a charger, which limits charge current, it's a power supply capable of supplying high current.
If, say, it's a 100A DC-DC, the battery's internal resistance is the only thing limiting that 0.6V (or whatever) difference between full charge of say 13.2V and the DC-DC 13.8V setpoint.
The internal resistance gets toasty as the square of that current. 100A battery charging has 2500 times the power dissipation in the battery as 2 amps.