Turning on Apple TV with HomeKit does not turn on TV

I found my problem: the Apple TV in question was logged into iCloud with another Apple ID. Just selecting the right user in the recently-introduced multi-user selection doesn't do it; you actually have to log out and back in with the same Apple ID used everywhere else. I kinda knew that, but forgot in the heat of the battle.

Update: Curiouser and curiouser... When I give the Siri command on my iPhone, "Turn on the TV in xxx", it works perfectly. But not so if I punch the button in the Home app on my iPhone. And the button on my Apple Watch has a red note, "No Response"; I get a similar response if I give a Siri command on my Apple Watch. And, in trying all this out, I suddenly would get an access code displayed on the TV in question, to be entered on my other Apple TV, which is serving as HomeKit hub (which got me trotting upstairs and downstairs a few dozen times - who says these devices are making us lazy? ;-) Anybody have a clue of what's going on??

Yet another update: punching the buttons in the Home app, either on the iPhone or on the Apple Watch, appears to be interpreted as "Stop / Resume", not "On / Off". Which probably explains why the attached TV does not come on. So I guess that works as designed. What I still don't understand is why the Siri command "Turn on the TV in xxx" works on my iPhone, and not on my Apple Watch.