Parent pigeons should have access to food around the clock. they should have food and water, in spill proof little bowls inside their nesting box. This is necessary for the overall health of both parents and babies, AND babies learn to become self-feeding earlier because they watch their parents. They too, will start to pick at the seeds in their nesting box.
It is always best to seperate breeders from racers, they should have their own seperate loft. Don't fly the parents until the babies are grown up and self sufficient.