I always took the livia being sent to gaius's chambers just as a private scolding from Gaius because of her actions in the waking sands and her failures at castrum centri. Despite how she captured minfillia and all that I don't think gaius actually ordered her to go and kill nearly everyone and to capture the leader, she likely did it on her own to 'prove' something to gaius and while her plan succeeded gaius may not have liked the method or the action out of order. A plan from gaius would be a little more subtle imo.