I too have a 70 inch Vizio P series tv (P702ui-B3) and my Apple Tv can turn the tv on and adjust the volume however it cannot turn the tv off. Also the auto off feature doesn't really seem to be working for me either as it can take 30 minutes or more for it to show "No Signal" and even then if often doesn't turn off in ten minutes.
I also have a PS4 and Onkyo TX-NR636 and practically the same issue where those devices can turn the tv on but they cannot turn the tv OFF.
Vizio has publicly stated they fully support all CEC features: https://twitter.com/VIZIOsupport/status/662645032898416640 however their customer service/tech support has practically said everything but the fact they support it.
From researching it appears some Vizio Models have no issues. Almost everyone with a P series however ONLY has an issue with powering off via CEC. I've also emailed tech support and they suggested to call which as stated truly got me no where for the time being. If you do call the reps in South Dakota seem to be more knowledgable versus some other places (they state their location when they answer the call).
I've also personally contacted them on Twitter (the above link was not me) and I received some DM's and they stated it should work and would look into it however I'm not holding my breath.
I've also submitted feedback to apple. Even though this isn't an Apple issue from my testing I've seen situations where Apple has proactively contacted other companies to ensure devices work well. One example is I know from an Asus rep who releases beta firmware onto one of their forums has acknowledged they've worked with Apple regarding iOS WiFi issues in the last year.
So my two cents is to reach out to both companies both written and via phone because when I called in not a single person with Vizio had heard of this nor even knew it was possible to turn a tv off via CEC.