That post is from 9 years ago. Also, every case is different. I've seen many asylum-based experiences where the interview was nothing more than swearing-in, verifying time outside the US, and the civics questions. 10-15 minutes and they're out. It all depends on the individual case, how complicated the asylum case was, if there are any red flags, etc. Heck, the same IO could either go very easy on your or be a total a**hole depending of whether they have had their morning coffee or not, LOL. There's no telling.
"Usually" citizenship interviews are to make sure you fulfill the requirements post-green card. However this is for EVERYONE regardless of how they got their GC. But yes, they can and sometimes review the ENTIRE immigration history. I know someone who had trouble at the citizenship interview bc of some weird stuff in between student visas. This issue never even came up when they adjusted to permanent resident.
So it all depends on your individual case, the immigration officer, and how the planets are aligned that day.
As for your brother, he shouldn't have to prove his claim of asylum all over again, but if the IO has any questions about something, they could ask him about certain things. If he's concerned, it would be a good idea to go over his entire immigration history, including his asylum application, and review any dates, events, names, etc., as a refresher. If he had an attorney or submitted any waivers, it would be a good idea to review those notes and see what language was used, and stick to that if those come up during the interview. Best of luck to him.