Sea Turtles tend to come ashore to lay their eggs during high tide. They also tend to do it during ALL phases of the moon, but they usually prefer a dark beach with little human presence. If they see humans, they will often either stay in the water or turn around and go back into the water.
Hatchlings emerge from the nest at various times. Though a favorite time is often around the new moon. Digging out of the nest is a group effort, but then they will usually sit a little bit below the surface until it is dark. Once it is dark or sometimes when it rains, they will complete their self excavation and burst forth from the nest. Sometimes only some babies will come out on one night, and more will come out of the same nest on the next night. The reason they emerge during darkness or rain is because they don't like the heat of the summer sun, which kills them quickly, and there also tend to be less predators in darkness and rain.
Once the hatchlings emerge, they are attracted to whichever horizon seems the brightest to them. In the absence of people and artificial lighting, this brighter horizon is the sea, and they head for it. With artificial lights in the area, they often get lost and die. So the Vero Beach resort limits the lighting that faces the beach.
As soon as the hatchlings hit the water, they start a 'swim frenzy' where they swim continuously for 18 to 36 hours. This is so that they can reach very deep water, and disperse away from the beach and predators. After that, they drift around in the currents of the Atlantic Ocean, typically riding with clumps of seaweed, and they often settle in the Sargasso Sea for a couple of years, before they return to breed on the same beach where they were born.