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No, you aren't correct. Many are wrong about which two towers are referred to, because there are so many towers it could be in the story, and Tolkien predicted that.

Tolkien's Two Towers are actually Orthanc and Cirith Ungul, the watchtower where Frodo ends up at the end of this segment. Tolkien was against splitting the story into three parts, and didn't like the name. He thought it would be confusing, but the publisher insisted.

And PJ has it wrong too. In the early trailers, the towers were identified as Orthanc (Saruman) and Barad-Dur (Sauron)... We shall see if they corrected it or not. I am sure many fans wrote in about the error.