I have seen this in sefardi shuls but I am not sure as to what the reasoning behind it is. By kaddish, (yasom, to be exact) the entire congregation sits down. Usually by Ashkenazic shuls it is generally accepted that all will stand up for every kaddish? Why do the halachos by sefardim vary and why specifically by kaddish yasom?
Along the same lines you noted the contrasting customs between Ashkenazim and Sefardim, Rabbi David Sperling writes:
There are different customs about standing or sitting for Kaddish. The Rema writes in his additions to the Shulchan Aruch (O.H. 56, 1) "One should stand when they answer Kaddish". This is, as you wrote in your question, because it is counted as "words of holiness" ("dvar sh'bekedusha") which should all be stood up for (see the Rema ibid). However the Mishna Brurah there writes that there are those who say one does not have to stand for Kaddish, unless one was already standing. So, for example, the Kaddish after Hallel, when one is already standing because of Hallel, one should remain standing. This is how many Sephardim rule (see Yalkut Yosef, volume 1, p. 95). The Mishna Brurah rules that one should be strict and stand for every Kaddish.
Apparently, the custom of sitting may stem from not being obligated to stand, as Hacham Gavriel quotes "The Arizal was not Makpid to stand during Kaddish (Shaar Hakawanot Daf 16 Amud 4 based on the Kaf HaHaim 56:20 and the Sefaradi Aharonim all agreed to this Pesak)."