This is the one where you're rescueing ternie right? As it played out for me, as soon as I got near the abandoned msf base, the guy there started begging for his life and told me to fly to the pirate base to the north. When I got there I shot everything up (like you do
) and "won" the mission.
See screenshot for the in-game mission log from that mission (the next objective is simply "leave system").