It is normal for the water dispenser to leak a few drops (less than 1cc) of water after being used. You may also notice water dripping after dispensing crushed ice. This is also normal because tiny pieces of shaved ice stick in or around the ice chute. As the ice melts it drips down in the dispenser area.
Newly installed units can take up to 24 hours to cool down completely. Especially during this time, the plastic water tank contracts and expands as the temperature changes. In addition, when room temperature water enters the cold water tank it can expand and contract. This can also cause a drip from the dispenser.