iPhone Personal Hotspot always visible even when off

I was surprised to see my iPhone 5's personal hotspot available as a WiFi choice from my iPad. I checked the phone and personal hotspot was turned off. I turned it on and off again and it still appeared. Using Airplane Mode and rebooting the devices did not help - it just would not turn off.

This is intentional behaviour since iOS 8.1. It is called Instant Hotspot and is described as a feature of Continuity:

If you’re out of Wi-Fi range, your iPad or Mac can connect to your phone’s personal hotspot when your iPhone is close by. With the new Instant Hotspot feature, you’ll see the name of your iPhone in the list of Wi-Fi networks in Settings on your iPad and in the Wi-Fi menu on your Mac. Just select it and you’re connected. And when you’re not using your phone’s network, your devices intelligently disconnect to save battery life.