Additionally, you are not destroyed when reduced to 0 Hit Points. Instead, your life energy attempts to keep you active even in dire straits; you are knocked out and begin dying when reduced to 0 Hit Points. Does this mean you roll dying checks like everyone else and when you hit dying 4 your dead? and need to have a Raise Dead or Resurrect Ritual? or are Automaton more like D&D Warforged were they just go inert and stay that way tell someone repairs them?
Yes, you need to hit dying 4. And in general if an ancestry doesn't explicitly say it operates differently than others, if functions the same.