Cyrillic has the capability for phonetic representation, though this may vary depending on the actual slavonic language.
However as Esperanto aims at being a bridge language, using a non-Latin transliterion defies its goal.
It could be used for Esperanto-names, where the context must be in the local script: "Esperanto-domo" in an urban subvention form. Or "Johano" in a passport. Far fetched, maybe for (phonetic) sample text in Esperanto for the native population.
So no, one will not ever see Esperanto texts in Cyrillic, Sioux, Katakana.
"(In-)Correctness" does not seem to fit the classification however.
There are just three transliterations of Esperanto:
- Braille (special Esperanto letters)
- Gesture language (spelling of letters)
- Stenography (like Unesteno)
And there still is the mangled latin transcription, where the Esperanto letters could be written, and are replaced.
About the prononciation: there are accents, but the individual sounds are well defined. There are slight variations, foreign influence by native language, or
preni (length and tone).