edit every download client entry you have in sonarr and set the category to tv
edit every download client entry you have in radarr and set the category to movies
thats all you need to do. transmission works fine
i use sonarr and radarr categories, but realistically it doesnt matter what they are, just so long as they are different - all youre going to do is seed from there. its not like youre going to setup radarr or sonarr to use those download paths as root paths.
the categories you set have no impact on moves or where they end up in sonarr/radarr - something else is going on if they do not move - so its time to set the log level to debug, wait for an import to fail, then post those logs so we can work out why its failing.