Unfortunately it is not possible to create such an "offline hot spot" with the iPhone. If your provider does not allow you to setup a personal hot spot, you cannot really get this particular product working like intended.
I would say though that the way this particular product has been made to work is very unconventional. The user interaction with ...
Because you have it turned on. You have assumed manual control of the hotspot.
It will, however, not sit there beaconing all the time, because that would eat the battery. It will beacon for a time, then stop. When you enter the settings dialog, it begins beaconing again.
Make sure both devices are logged into the same AppleID, make sure Bluetooth is ...
I was annoyed by this battery-saving feature of iPhone tethering for over a year. What it normally does is to drop the connection when the traffic was not intensive enough, for example downloading a huge file vs. watching YouTube video with buffering.
After searching around, I found the following methods that actually work!
Tethering over a USB