The Director is a god that people created in the future. The Travelers are following its orders, struggling to stay within its "commandments" (the 6 protocols). The faction is a splinter sect. Grace's trial was essentially a trial for heresy. By rebooting the Director, she re-interpreted the" sacred text".
i think you might be confused by the scene where it showed many old people speaking to grace. the director is an AI created by humans to help them survive. The director seems to only be able to communicate directly to humans to the bodies of those who are going to die (usually the elderly) or children (messagers).