All nations of the world maintain their own Registers of Civil Births in which a birth (within the boundaries of that nation ) is recorded automatically. It does not matter if the parents of the baby are its nationals or not. It also does not mean a baby is automatically a citizen of that country, unless this particular baby ( born to foreign parents) on attaining adult age claims for himself/herself the citizenship of the country where he/she was born.
It has been my belief all this time ( and I could be wrong) that the Portuguese had left Goa in a hurry and had no time carry along with them copies of the Registers of Births ( that have taken place before 19th December, 1961) they maintained in Panjim, Margao, Vasco and Mapusa and hence Goans were at liberty to re-register their births in the Goa related Civil Births Registers now maintained in Lisbon. It is my personal opinion that mere re-registration in Lisbon of births taken place in Goa prior to 19th December, 1961 does not necessarily mean that one becomes a Portuguese citizen. One has to apply further for a Cartao de Cidadado (something alike our Identity Card for voting purposes) and based on this Cartao one could apply for a Portuguese passport if one wishes.