They often ignore enemy ships flying right past them, but also often fly to the other side of the galaxy at breakneck speeds to kill some random maintenence ships. They also tend to lock on to ships that are on a quest and camp near the galaxy border.

They will try to attack the ship with the highest level :) If they are friendly, they will escort them around instead.

They shouldn't chase those who've left the galaxy though, I just fixed that, will be in the next version.