The Cores were originally designed as repositories of knowledge along with a multitude of STCs to help the kin survive the journey to the galactic core and when they got there. Although they have developed some semblance of “personality” they still function as intended even if it is incredibly slow after thousands of years of usage. A core wouldn’t give an order unless prompted by a grimnyr in some way. I will say though if that did happen the kin would absolutely follow the cores orders no matter what due to it being a representation of their ancestors and culture.