The USSR didn't send local teachers to the satellite countries. They probably could have done it: a quick demographic calculation shows, some thousands of native Russian teachers had been enough for ten million people in the satellite state. It is far lesser, as the "temporarily by us stationing allied forces", what was an euphemism for the Soviet occupants. They were in the order of 100 000 for ten million people.
Inside the Sovietunion, the situation was quite different. The CCCP utilized a large mass of (Russian, but also other) teachers, intelligentsia into the non-Russian speaking member states, with the goal to dissolve their culture in the CCCP. (After the collapse, they became a Russian minority, being nearly so hated as the Russian teachers in the satellite states.)
Of course, it didn't happen on a voluntary basis. It meaned that a part of the newly graduated people was simply sent to remote, underdeveloped, foreign language-speaking regions by command. For them, it was essentially exile.
Also I was thaught Russian in the classes 4-8. It was extreme unpopular, being a Russian school-teacher was a "dirty job". Sometimes intentional sabotage of the courses was not unheard. We all hated it. Even the few people learned it well, they did it because they've learned everything well, and not because they had loved it.
Being a Russian teacher had meaned, that you are "a man of the System". Like a membership in the Communist Party.
In the first years after Russian was made obligatory, there was a very big lack of teachers. All the schools had to hire them, following the law, but there weren't enough of them. Many times it happened, that teachers without a Russian knowledge were hired, they learned Russian as they've teached it, and many times they knew only a single lection more, as the class they've taught.
Later they became better, also in quantity as in quality, but the universal sabotage of the Russian remained until the end of the communism. Hadn't they collapsed, maybe we had adapted in some decades.
After the collapse, the same process happened, but with other languages (English and German). Everybody wanted to learn English and German, but there wasn't far enough teacher. But there was a large mass of Russian teachers, all threatened by the danger of the unemployment. Typically, teachers had qualification for two classes, thus the situation wasn't so bad for them, but the English/German teachers were still missing. On these reasons, most of the schools still made obligatory the Russian for some years, as a local privison, even if it wasn't obligatory by law any more.