If you hatched the cygnets without the parents, the adult swans may not accept the cygnets and try to harm them.
If the cygnets have been kept with the parents from the time of hatching, then their should be no problem with the parents accepting the cygnets. The cygnets should be kept with the parents from day one.
Once all eggs are hatched, realistically, all cygnets can be released onto the pond after 24 hours from the last hatching. Within 24 hours of hatching, the mother swan will take the young cygnets onto the pond. This is the realistic timing. However, if you should have many predators, i.e., snapping turtles, egrets, herons, large mouth fish, owls, hawks, and other predators, you may want to keep the cygnets and the parents in a secure pen. Now, having said this, even though you are protecting the swans from predators, you may be increasing the possibility that the family could be susceptible to injuries and disease while penned. So, you have to weigh these factors, but the best may be to release them onto the pond and let nature takes its course. The cygnets must learn from their parents the basics of survival and how to be a swan. The Regal Swan