Nah. I'm wrong. The laptop started that way, probably because the keyboard is attached to a CalDigit dock, and tapping on the keyboard probably sent power to the device, which starts it.
That doesn't happen with the Mini, if I actually do a shutdown from the menu.
Apple has something I think they call "Deep Sleep," which is basically a shutdown, and that wakes from the keyboard.
That said, it's not a big deal to reach under the left side, and tap the button. The laptop was a pain, because I had to open it up.
But I've only had this thing a few days, and haven't had a chance to really torture it, yet.