I have noticed that if I'm running Anki and other QT-based applications such as qutebrowser from MATE's start menu, Brisk Menu I can't switch to and input Japanese using fcitx-mozc (I haven't tried ibus-based inputs though), but running them from the terminal I can.
Couple points I noted while searching around the web which might help with this issue:
Of course, it could be something else.
Edit: I have tried Ibus-mozc too, but strangely enough I can't seem to be input anything into Anki even if its launched from the terminal. (I like fcitx better though)