Most ISPs function in the same way. The exception is that a handful of ISPs display all their users as behind the same proxy, but SWC distinguishes that, and those users don't need to register, since they would need to register with every other person using that ISP at all.
So the easiest way is just to ask any SWC assistant, instead of pestering your ISP and trying to interpret what they tell you. We can check your IP address, we can check if you're using a proxy, and we can compare the IP between two accounts.
The general guideline is that you need to register if you are using the same immediate connection as another SWC player. This means if you share a computer, or if your computers are networked and connect through the same router, you need to register. If neither of those are the case, and you never share a connection (meaning you never log into SWC from the other person's connection) you don't need to register. It is pretty straightforward.