That's a citizenship thing though right? The Republic is of the opinion that everybody on Ireland† is a citizen of the Republic. If my mother had happened to be in Portavogie when she gave birth to me last century, my understanding is that the RoI considers I am automatically a citizen, because I was born on "their" island even if certainly Portavogie is not under their control.
† The exact rules are complicated, but they don't depend on where on the island you were born or stuff like that.
† The exact rules are complicated, but they don't depend on where on the island you were born or stuff like that.