Hi Tuongvan In American English, saying "tuition fee" would be redundant. I would not add the word "fee". Look at this .
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TuongvanBut I often see the present perfect used with reporting verb to express an action that is still continuing at the time of speaking.Tuongvan:
They said five people have been arrested
So I think "The tutor complained that Mary hasn't paid for two months." is ok here