I posted this same topic last week but put wasn't sure then as I thought I must have brushed the X1 power button while plugging stuff in for the 360. But I put my 360 console away again last week but just now got it out AGAIN and this time when I turned the 360 console on, the Xbox One definitely switched on and the Xbox One logo appeared on my TV.
Go into the settings of the xbox one and see what it says. Will be under system or something, I don't know off the top of my head.
it came on when I pressed the 360 power button - they both powered up simultaniously. I don't think the Kinect had anything to do with it. I thought it might be to do with my router as they are both connected to it and might somehow trick each other into thinking that they are the same console. Or something.