There is a setup process. Again, once you've run the setup, you're all set (link fingerprint scanner). It has you say "Hey Siri" three times and then a phrase once or twice.
Yesterday, I tried to use Hey Siri on my watch. I held the watch up to my mouth and asked my question. Siri did activate, but misheard me - as so often happens. Happily, my iPhone 6S was sitting on the table a couple of metres away, also activated Siri, heard me correctly, and gave me the answer I was after.
Mine works fine. It responds to my voice and didn't when I held the phone close by to hear that YouTube demonstration. I'm wondering it the recognition ability will improve with time for those who's phone can not discern their voice from others.
What I find unusual is that the iPhone needs to be face-up when laying on a table near you. Since mine is always in a case with lip protect, I tend to place it face-down. Not sure if I'll change my habit or not.