Why do you think that they are wrong ?

As visible on this page, it is broadcasted started from October 5 at 25:05 on Tokyo MX, which means from October 6 at 1:05 in the morning.

When you check the air times on the following sources you see different air times: Crunchyroll https://www.crunchyroll.com/watch/G50UZX49G/rebels-acting-in-secret Anidb (bottom of the page) https://anidb.net/anime/17695 TVDB https://thetvdb.com/series/boukesha-ni-naritai-to-miyako-ni-deteitta-musume-ga-s-rank-ni-natteta/seasons/official/1

For example the air time for episode 6 of this show is November 10, 2023 but it has already aired on November 2, 2023.

@KingHawk said:

For example the air time for episode 6 of this show is November 10, 2023 but it has already aired on November 2, 2023.

We only take in account the regular Japanese TV broadcast. We don't take in account the digital previews.