There is no rule. It tends to follow the form of the name of the country by which it is known internationally. In the case of Fiji, I have no idea which language influenced the use of the plural. Indeed, checking two dictionaries, one has only Fiĝioj (PIV), and the other only Fiĝio (ReVo). In any case, there's no logic to this, some things just have singular or plural names, just like in English.
La Akademio de Esperanto recommends Fiĝio.