TeamSpeak ignores localized directories on Linux, and creates separate “Downloads“ directory.
Most Linux desktop environments support XDG Base Directory Specification with xdg-user-dirs. So mostly Linux programs use value from XDG_DOWNLOAD_DIR environment variable, or read values from “$(XDG_CONFIG_HOME)/user-dirs.dirs”, if it doesn’t exists, then “/etc/xdg/user-dirs.conf”. This values already has localized paths to standard directories.