Yes, I remember trying to remember to use Jekavian as opposed to Ekavian when travelling through Croatia some years back. The last time I was on holiday in Montenegro, I remember seeing both forms on official signs.
When I was in Leningrad, one of my room-mates was half-Azeri. I recall her scorn when she heard that a Russian lecturer had told the Brits that the Soviet Union had gifted the Azeri the Cyrillic alphabet because there was no written form of their language...She explained that they had previously used a form of the Arabic alphabet and that she had been taught it by her grandmother.
I'm unclear as to what the official Azeri alphabet is now. I don't know about what happened in Tajikistan, but I wonder whether it was a case of the Russians imposing their alphabet on the other nationalities as a whole.
I seem to recall that Mongolian is written in Cyrilic - or at least it was in Soviet times (even though it was just a satellite state).
When I lived in the Moris Torez Hostel in Moscow, previous students had put a sign with "Mongolia" written in Cyrillic on our room door. The result of that was that an irate Russian hostel manager brought a couple of new Mongolian students to our room and demanded to know why we'd put that sign.
Certainly, my impression was that for all the speech about equality etc, Russians could be quite patronising towards other nationalities. [Also see: "Ukrainian is just a dialect of Russian"...]