Попробуйте обратный вызов onUserLocationChange и установите свой регион соответственно с помощью setState
state = {
showsUserLocation: true,
followsUserLocation : true,
mapRegion: {
latitude: 37.78825,
longitude: -122.4324,
latitudeDelta: 0.0922,
longitudeDelta: 0.0421,
},
};
<MapView
style={{ flex: 1 }}
region={this.state.mapRegion}
//use this callback to update the regions
onUserLocationChange={event => console.log(event.nativeEvent)}
showsUserLocation={this.state.showsUserLocation}
followsUserLocation={this.state.followsUserLocation}
/>