I like a lot this view I often noticed in writers - especially fiction writers obviousy.
You kickstart a story with your idea but then the story takes a life of its own. The characters develop a personality. In your head as an author they start becoming self-consistent and have an identity of their own. We humans are masters at putting ourselves in the shoes of others including others that don't exist. In a very real sense our characters take life through our imagination and the stories we put them in.
Why does it work like that? At the end they are projections of ourselves, aren't they? Well yes but even projections develop a history that we then remember, they had specific interactions which reveal a character that we didn't plan for but that develops as the story evolves. And like most things we can't forecast that up front so they have as close as we do a concept of free will.
It's amazing how reality and fiction develop in similar ways. One moment at a time, one action at a time. One story at a time.