The increase in kinetic energy leads to leakage of water from the syringe.
When the outside temperature is more than the liquid temperature, say the syringe is out in sunshine, then the liquid becomes slightly warmer. An increase in the temperature of the liquid will lead to increase in the kinetic energy of the particles and they will star moving faster. In other words, the expansion will lead to increase in volume of liquid, similar to expansion of metals when heated. This increased motion will lead to water molecules pushing each other, as a result of which some of them would be pushed out of the syringe. This will give rise to the formation of a little puddle of water under the tip of the syringe.