WiFi Browsing

I've had this issue with previous models and for once and for all, I am posting here to see if I can get an answer. I open up my Hotspot Browser on my home wifi network from my BB and it says "You are now connected to the Internet". The Wifi Logo is lit up white, and I confirmed I am connected through Wifi options. I select in the same "You are now connected to the Internet Browser", Go To, "Whatismyipaddress.com" and it shows RIM's public IP's. If I am going through my Wifi Network, shouldn't it show my home Verizon IP? Or does it use your wifi to connect to the RIM network and then surf out? I also tried hitting my wireless router and camera private IP addresses on my LAN from the hotspot browser and I get HTTP Error 504 Gateway Timeout. Any ideas?