A place to go on this question may be the 1997 book The Black Book of Communism: Crimes, Terror, Repression is a 1997 book edited by Stéphane Courtois. It's a French book with a good English translation. Franco, by English historian Paul Preston would also be of assistance.

Anyhow, what you'll generally find is that the outbreak of the Spanish Civil War followed a sliding deterioration of the political situation and fairly early on, if not immediately, the term "Republican" included a variety of political views on the left which were dominated by Socialist and Communist of various types, but also included anarchist and regional separatist. As The Black Book details, the Soviet effort was part of an overall program of backing the communist left where it could. As the Republicans included other elements other than the communists the Soviets actually erred by sponsoring clandestine acts against the other left wing elements at the point at which they thought a Republican victory inevitable, the thought being that in that manner the communist would come out on top. In reality, they acted too soon (and given the way things were generally going maybe that day would never have come) weakening the Republicans somewhat at that point.