Ok, so the app gives the watch a phone number of its own without the need of a sim card, so when you use it to call someone, you will call from that number and not from the number of your phone.
Jason doesn’t mention bluetooth, so I don’t know why you got the impression that it uses a bluetooth connection. All it needs is a connection to the internet, so it can be connected through your home wifi, wifi hotspot from the phone (this is what Jason mentioned) or possibly you might be able to share the phones internet connection through bluetooth. I think some users here have succeeded in sharing the internet connection through bluetooth, but it seems to be difficult to get it working.
Also, look at the following post where @roswell108 mentions a similar app: