It was always Cyrillic. What OP meant is that there were plans to switch all Soviet languages, including Russian, to Latin at one point - this was considered beneficial by "first wave" Bolsheviks, who believed in worldwide communist revolution in near future, and unification in a single world state, and assumed that Latin would be the common script of that state.
Later, when Stalin ditched all that, and came up with "socialism in one country" and revival of imperial patriotism, these attempts were scrapped, and Cyrillic became the common script for all Soviet languages instead (even those that were already Latinized). This was in line with the new national policy, which presented the Russian nation as the "bigger brother" of other ethnicities, e.g.: https://www.marxists.org/reference/archive/stalin/works/1945...
Not exactly all of them. Lithuania, Latvia and Estonia retained Latin script for their languages, and I think Armenia (which is now using its own alphabet) used it during Soviet times too, though I am not 100% sure.
Armenian and Georgian had their scripts. So at least 5 SSRs out of 15 had their official language in non-Cyrillic script, who knows how many other languages did too.
Later, when Stalin ditched all that, and came up with "socialism in one country" and revival of imperial patriotism, these attempts were scrapped, and Cyrillic became the common script for all Soviet languages instead (even those that were already Latinized). This was in line with the new national policy, which presented the Russian nation as the "bigger brother" of other ethnicities, e.g.: https://www.marxists.org/reference/archive/stalin/works/1945...