Interestingly, we can actually see how Soviet citizens would consume their tobacco from studies like this NIH study, which says that over 80% of the cigarettes consumed were produced domestically, and that the rest of the imports were from Bulgaria (the study itself is from 1982). In addition, studies like this indicate that there were frequent shortages as a result.

We know, from primary sources such as this one, that towards the end of the USSR foreign companies were allowed to sell and export their products to the consumers there.