This has been happening for some time now. My Xbox One will turn on randomly. Sometimes, it doesn't make the sound when it turns itself on, I just happen to notice the light on my Xbox One and Kinect are both on. Other times it does make the sound.
I do not have the "Instant On" feature enabled, nor do I have the "Keep my games & apps up to date" feature enabled.
I do use the Xbox app on Windows 10 as well as on my phone, but as far as I know, these cannot turn the console on (they can connect to the console, however it needs to be on first before they can).
What could be causing this? I have considered the Kinect possibly turning the Xbox on, but why would it? My Kinect is no longer connected to my Xbox and it still happens.
Edit One: This is still happening after numerous updates - 4 months later.
Edit Two: About 5 months later this is still going on. Do Xbox One's have some sort of Wake on LAN feature that is hidden? I'm beginning to wonder if it is attempting to download an update for the software similar to how Windows does. I've experienced something very similar with my Windows 10 PC turning itself on to download an update (but not install it until I manually restart).