Quite normal, when you connect to a vpn the adapter should obtain an ip address for the remote network which is different to your local ip. That ip is the one that then goes out via the remote gateway.
For example a corporate hardware Vpn I look after, when a user connects we distribute 10.0.0.x with routes to the local network at the vpn side (192.168.101.x). Effectively you have 3 ip addresses, your local v4 addy which is likely 192.168.1.x, the remote local ip (highlighted yellow) and the remote gateway or public facing IP (in black).
The ip in yellow i.e. the remote local (to the remote network) v4 addy will likely increment as a user connects the vpn (is just a dhcp pool of addresses). The one in black is the remote gateway which doesn't change.
In simple terms you need an ip on the remote network that is in the correct subnet and is configured to hit the remote gateway. No doubt somebody can explain it better but it is a standard VPN config.