No, it shouldn't have inversion. The sentence "Echter, kent ze daar niemand" is still officially incorrect, so it should have been suggested bu Duolingo. Nowadays most Dutch people use it that way (although without the comma), but the correct form is "echter, ze kent daar niemand".
"However" is not necessarily postpositive. It can come at the beginning, in the middle or at the end of the sentence. The different positions result in different emphasis, slightly different meanings. Some frown on starting a paragraph with "however." We have no context for this sentence. The "however" could well be related to a preceding sentence.