iPhone 5S Personal Hotspot sometimes automatically turns on
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.