Home Assistant is the brain of the operation. Your smart phone is just an arm or hand in the operation. It’s the same for any of the services you perceive to be just using your smart phone. They actually call out to servers owned by the various companies, and then return requested operations to your devices at home. So with Home Assistant you have the opportunity to use devices and a server that all remain in your own network. Your data and information aren’t being sent to a third party. This, of course, depends on the devices you buy.