Okay, here’s a story. I was so nervous about CSSSA that I started freaking out, thinking that I hadn’t had adequate preparation in my English classes. So I spent the weeks leading up to CSSSA speed-reading through a bunch of classics that my school had neglected. I read as many as I could, and when it became obvious that I couldn’t read them all, I read about halfway through them and read the summaries online. I don’t even know what part of my brain thought that was going to help me, but it was WRONG.
Long story short, I don’t think you need any preparation. Practice writing in the weeks leading up to CSSSA. Try writing a little bit every day, just to get in the habit. But as far as the teachers referencing specific works… that rarely, if ever, happened. And if it did happen and you didn’t know what they were referencing, it wasn’t detrimental to your understanding of the lesson being taught. They’re not going to expect you to have read every single book ever. They just want you to understand that there are different styles of writing, and YA novels aren’t the only thing out there.