It generally doesn't matter who you call. The call and rescue efforts will be directed through the designated control centre.
This kind of rescue redirect is especially common now with the advent of EPIRBs (Emergency Position-Indicating Radio Beacons) which are registered to a particular country/authority, but work anywhere in the world. If your Lisbon-registered is activated far enough off the coast of Ecuador to be in the SF zone (and assuming the map is correct), the ARCC Lisboa will contact the SF MRCC and they'll co-ordinate the rescue effort.
This kind of rescue redirect is especially common now with the advent of EPIRBs (Emergency Position-Indicating Radio Beacons) which are registered to a particular country/authority, but work anywhere in the world. If your Lisbon-registered is activated far enough off the coast of Ecuador to be in the SF zone (and assuming the map is correct), the ARCC Lisboa will contact the SF MRCC and they'll co-ordinate the rescue effort.