Any website or internet service you touch will see your IP
address. That' is how it can communicate back to you.

For the systems that 'anonymize' connections there are two
basic techniques. One is a masquarade system. You contact the
anonymizing server, along with many others, and it contacts
the remote site and relays the stuff to you. (Local networks
with NAT work like this, too.) The other system is uses a
network of cooperating computers. When you make a request it
might come right from your computer or it might be relayed
through one or more cooperating computers. And those other
computers will relay stuff through you, too. Afterwards there
is no record of which computer in the network issued the
original request.

I like this bit at the end of the article:
"I think they're trying to scare people," Barnes said.

Nice understatement.