Am I correct in thinking that the use of Russian “Tsar” implies that at least some Roman nobility fled in that direction during/after the fall of the Empire?
The reason for the use of "Tsar" is Moscow being associated by some as being the "Third Rome", after the fall of Constantinople in 1415 (which was called by Constantine the "Second Rome"). Russian Tsars saw themselves as the continuation of the legacy of Rome and saw themselves as being in the legacy of the great Caesars of the past, so they adopted the Russian version of the name, calling themselves "Tsars." Hope that helps clear things up for you! ;D