It's a great question. The simplest answer is prison chatter. Even though Sinestro is behind an extra security door it wouldn't be surprising that he had some occasional contact with a prison guard. It's also possible a Guardian or someone more important occasionally comes to him for information similar to what Hal is doing.

The other option is that John is a long term plan by Sinestro. Look at John's father and upbringing. John's dad is raising him to not be afraid, the "perfect" Green Lantern. But how does John's dad know that is the training? The interview is the first time Hal is officially going public. It's clear John's dad has been shooting at John for a while.

John, as a replacement Green Lantern, is Hal's biggest fear. Sinestro has just been waiting for Hal to show up. He isn't surprised to see Hal. He, directly or indirectly, positioned John Stewart so he knows who he is.