When your tank is full it goes out the overflow lines. It will continue to flow out until the pressure in the tank has been relived. Be careful not to keep filling because the overflow cannot keep up with the flow of the hose. As soon as the overflow starts to have water come out, turn off the water.
As you travel water may still spill from the overflow lines. I do not travel with water in the tank do to the fact that Heartland built mine with 6K axles and its weigh is almost 12K on them without water. I do not fully load with food and pack light on clothing. My friend does fill his with water and he ends up with 1/2 to 1/3rd of a tank of water when he gets to his destination. Some other Heartland owners have had the same problem and have added shutoff valves for traveling. You must always remember to open them up. If you don't, you may burst you plumbing or tank when filling.