Poor Cell Signal

You're confusing AT&T's Cell Booster with a cellular booster. What AT&T offers is a femtocell, not a cellular booster. The name is misleading but that was a marketing decision. Most people have an idea of what a cellular booster is but not a femtocell.

The Cell Booster has very little to do with the local cellular tower, other than location verification, handing off, and maintenance. The Cell Booster uses your internet connection (DSL, cable, or fiber) to connect to the AT&T MobilityServers. It will broadcast an LTE signal that your phone can connect to as long as you have a post paid AT&T cellular account and a phone that meets AT&T's post-3G cellular requirements. There is no cost other than the initial purchase of the cell booster.

WiFi-C (WiFi Calling) is really preferred for improving poor in-home reception, as long as your phone supports WiFi-C and you have a good WiFi connection in your home.

A cellular booster is an antenna that attaches to the outside of your home and detects the outside cellular signal (as long as you can get 1 and preferably 2 bars of consistent signal strength) and, via a cable, brings the signal into your home, boosts it, and attaches to another satellite that broadcasts the cellular signal.

I have two Guides linked in my sig line. The first one is for AT&T's Cell Booster and the second one is for Cellular Boosters. A bit technical but they will give you an idea of what each can and can not do.