At present, the bird you’re talking to has to, itself, be able to talk to a ground station. This means that you have to be within about 450nm of a ground station for the system to work reliably.

Note that this distance limitation will go away (technically) when the sat/sat laser-mesh goes active, probably towards the New Year. However, while there’s no technical reason the RV systems can’t use this mesh, it’s not clear who will be allowed to use it & who won’t.
There are 2 ground stations in Puerto Rico, & they cover the whole of the eastern Caribbean, with the exception of Barbados & Trinidad. There’s a new station in Ecuador(?) that is providing coverage to central America. While the San Blas seems to be working, folks have reported poor coverage in Panama itself (not sure why).

There are no ground stations that we know of in the South Pacific except the one installed near Suva to serve Tonga, but I’m not even sure that it allows service from Fiji. Countries that haven’t signed at least some level of agreement with Starlink can be geofenced, & that might be happening in Fiji.