Why does my Macbook Pro "see" my iPhone Personal Hotspot even when it is turned off? And sometimes, my iPhone Personal Hotspot gets turned on automatically. What is happening here? This does not happen often, and when it does, it is usually when the WiFi signal is unstable. 3G is always there as a back up, so I don't know why my phone is trying to cover for this unstable signal.
It seems you're seeing the "Instant Hotspot" feature available on the devices running iOS 8 or later. It's a part of Apple's continuity features that lets you share the data connection from your iPhone or iPad (cellular) to your WiFi only Apple device. It uses your Apple ID for authentification, BT LE for connection and Wi-Fi for data transfer. Thus, it's different from a personal hotspot, which required a password. You can read about it here: https://support.apple.com/en-in/HT204681#hotspot
As of iOS 9.3, you cannot disable the Instant Hostspot. Only way is to call your carrier and have them remove the feature from your account.