Dan Moren points out that, with the new iPhone 6S/6S Plus, you can temporarily deactivate the always-on “Hey Siri” feature, wherein Siri wakes the phone and listens for your instructions, by putting the phone face down.
What he doesn’t mention is that this works on the older iPhone 6/6Plus models too, if Siri is listening for the command – such as when the power cable is connected, or if you’ve already activated Siri. The face-down trick might even work on the iPhone 5, but I haven’t tested.
In other words, put your phone face down when charging at night and there’s no risk of accidentally triggering Siri.
Myself and my partner both have iPhones and often I will use the Hey Siri feature at night when our phones are charging on our nightstands (bedside tables, to us British). If I said “Hey Siri”, then both our phones would wake. Now we can stop that occurring, although the Hey Siri voice training in iOS 9 also helps.