History

I don't know who ordered the deaths of the Romanovs but I can inform you on their likely reasoning. In the most simplistic sense Russia was a monarchy for centuries and its populations, ESPECIALLY the peasantry were very used to this and did not have the educational basis to understand organized society beyond this format. This, combined with the fact that historically speaking leaving a member of royal blood alive after seizing power leaves room for counter revolution heavily informed the decision to straight up eradicate the Romanovs. From the perspective of the Bolsheviks, leaving Romanovs alive was too risky and honestly, with the counter revolution that insued after, I think they were right to do so. I cannot imagine how the civil war would have proceeded had the whites had a Romanov.