Of course you should not have to move the recorded audio, it should be in sample accurate sync.
When you start Cubase. do you experience a delay before playback starts? Also you may want to check the Remote Delay setting and try to raise it, usually 1 second should be ok. One more question: while recording, do you hear the performer in sync with the playback?
Sorry for the inconvenience but we’ll find out I’m certain.