Reptile eggs are fertilized at the point where the sperm encounters an egg in the oviduct. At that stage the eggs are very much like they are in a mammal. They are a minute, soft, cellular material. The fertilized egg then travels through the oviduct, building up coatings that the host (female) produces.
With reptiles there is typically an exterior environmentally triggered process that starts a hormonal process that begins the egg development.