In fact most newer machines can do this ( too many priors at https://www.google.com/#q=can+task+scheduler+turn+on+computer )
I'm still hunting down why my new Windows 10 laptop does this but there's a lot in task scheduler to wade through and my finding won't apply to your PC. But keep looking.
Be sure to disable WOL (wake on lan) too.
Lately my workstation has been powering on after I leave the office. I leave at about 5:45 usually and by 6:03 it is completely powered on. I know this by checking the Task Scheduler, it shows that Adobe updated at 6:03pm Last night, the only issue is I was already at home relaxing in my chair by this time.
Im assuming Task Scheduler is powering on the PC from a completely shutdown state, if not I have no clue how or why this is happening.
Any help? And thank you in advance.