The poskim argue about when one should remove his shoes if he is stringent to normally keep the zeman of Rabbeinu Tam. R’ Shlomah Zalman Auerbach held that since one is only keeping the zeman of Rabbeinu Tam as a stringency, on this motzei Shabbos one shouldn’t keep the stringency, and from half an hour after shkia he should keep the dinim of Tisha B’Av and remove his shoes (Halichos Shlomah, 15:12, and Devar Halachah s.k. 15). They bring further, that R’ Shlomah Zalman himself had the minhag to remove his shoes already from shkia and would lie down without shoes until tzeis hakochavim to avoid any doubts. He would lie down and not sit, as he didn’t want to sit on a low stall, as he didn’t want to show signs of mourning on Shabbos (Shalmei Mo’ed).
R' Elyashiv would remove his shoes before bein hashmoshas like every Tisha B’Av, as generally he was in his house at that time, therefore, it wouldn’t be considered mourning in public for him to walk around his house without shoes (see he’oras of R’ Elayshiv Mo’ed Kotan 24a, and Menashim B’Ohel pg. 148).
The Nitei Gavriel (94:1) writes: Those who keep motzei Shabbos 90 minutes after shkia (in Chutz La’aretz) can be lenient to wear their shoes until then, since until then it is the time of tosefes Shabbos. Some say (Shemiras Shabbos Kehilchosa, Perek 28, he’orah 189, quoting Shu”t Salmas Chaim, siman 340) that it was accepted that the time for removing shoes on Tisha B’Av that falls on motzei Shabbos was when borchu is recited, and until then the kedusha of Shabbos continues.
R’ Sroya Davlitksy (in his sefer Tisha B’Av Shechal B’Yom Rishon, siman 39) writes: The minhag in Eretz Yisroel from early times was to follow the opinion of the Geonim to bring out Shabbos forty minutes after shkia, and not to follow Rabbeinu Tam. Additionally, the reality of what is going on in the sky doesn’t really fit with Rabbeinu Tam (as it is dark long before that), consequently, even those who are stringent for Rabbeinu Tam every week, when it comes to Tisha B’Av and removing shoes one must follow the Geonim. Especially as removing shoes doesn’t involve chillul Shabbos, and it is better to me stringent with the restrictions of Tisha B’A, than it is to keep Shabbos when it clearly isn’t Shabbos.
R' Sroya Davlitksy adds: If one changes into weekday clothes during that time (between forty minutes after shkia and Rabbeinu Tam nacht) one should remember before Shabbos to empty his pockets from any mukzteh, since for one who is stringent for the opinion of Rabbeinu Tam it’s still considered Shabbos.
