It varies of course, in fact some species of birds don't seem to have a very pronounced synchronisation of hatching at all, and many chicks are lost as a result. Some birds only seem to start serious incubation after the last egg is laid, which helps with synchronisation. In species that do have pronounced synchronisation, and incidentally, in crocodilians as well, the unhatched eggs become vocal well before hatching. They can hear each other's piping, so that they have an idea of when to hatch and so that the parent knows when to expect them.

Experiments in which piping sounds were played a few days  too soon elicited  aggressive reactions from mother ducks, whereas piping on schedule elicited encouraging sounds that apparently imprinted the voice of the mother on the nearly-hatching-ready chicks.

Such communication gives unhatched chicks a few days' grace for the most advanced eggs to delay hatching while living on their yolks, and for the laggards to hurry up and emerge with some spare yolk to tide them over the first, hardest days in the open.

Regarding poultry, they hatch at similar times because they started incubation at the same time. This despite the fact that birds lay eggs over several days. You might think that the chick starts to develop immediately the egg is laid. However the incubation period only starts when the hen stays on the nest and the eggs become permanently warm. Until then the eggs are dormant and tolerate being kept at ambient temperature for days if not a week. This gives the hen time to build up a sufficiently large clutch of eggs. Once the hen sits continuously, then only do all the clocks start.