Twice in his presentation of the laws of Tzitzit (8:11, 24:1), the Shulchan Aruch writes that the Tallit Katan should be worn over one's clothing, so that he sees the Tzitzit at all times and thereby be reminded of the Mitzvot. According to the Shulchan Aruch, the entire garment of the Tallit Katan should be worn over one's outermost garments (like many Chasidim do today).
The Mishna Berura (8:26; commentary to the Shulchan Aruch by Rabbi Yisrael Meir Kagan, the "Chafetz Chayim," Lithuania, 1835-1933) strongly condemns the practice of those who tuck the Tzitzit inside their pants, rather than leave them exposed (listen to audio for precise citation). He writes that doing so not only undermines the purpose of Tzitzit "you shall see them and remember all the commandments of God" (Bamidbar 15:39) but also denigrates the Mitzva. The Mishna Berura adds that a person who received a garment as a gift from a king would proudly expose it for all to see; all the more so, then, should one make a point of exposing the Tzitzit. Those who conceal them, the Mishna Berura writes, will one day make an accounting for this shameful practice.
However, the view of the Arizal (famed Kabbalist, Israel, 1534-1572), as recorded and understood by his student, Rabbi Chayim Vital (Israel-Syria, 1542-1620), and by the Chid"a (Rabbi Chayim Yosef David Azulai, Israel, 1724-1806), was that the Tallit Katan both the garment and the Tzitzit strings should not be exposed. Chacham Ovadia Hadaya (Israel, 1890-1969), in his work Yaskil Avdi, cites other Kabbalists who followed this view, as well.
Therefore, Sepharadim, who generally follow the laws and customs of the Kabbalists, should keep their Tzitzit tucked into their garments. Chacham Bentzion Abba Shaul ZL (Jerusalem, 1924-1998) cited his mentor, Chacham Ezra Attia ZL (head of the renowned Yeshivat Porat Yosef in Jerusalem), as remarking that any Sepharadi that exposes his Tzitzit denigrates and casts aspersions on the previous generations of Sepharadim, who followed the practice of keeping the Tzitzit concealed. Rabbi Yehuda Tzadka ZL (who served as Rosh Yeshiva along with Chacham Ezra Attia ZL) testified that the esteemed Rabbi Yaakov Chaim Sofer (1870-1939), author of Kaf Ha'chayim Sofer, likewise kept his Tzitzit inside his clothing. The same is said about the prominent Kabbalist Rabbi Efrayim Cohen ZL, and this is the ruling of Chacham Ovadia Yosef, in his work Yechaveh Da'at (2:1).