AXI interface of an FFT core expecting more data than it should
The document you linked to confirms how I would expect TREADY to be handled. Page 51, paragraph 2 says:


  In particular, the behavior of TREADY on the input data channel [timing diagram] is not fully accurate because 
  the Data Input channel buffers the data (16 symbols in Non-Realtime mode and 1 symbol in 
  Realtime mode). However, this data waits in the buffer until the FFT processing core is ready 
  for it. The Data Input channel TREADY in these diagrams is used as an indication of when 
  the FFT processing core wants data rather than when the AXI channel (with its buffer) wants 
  data.


And page 52, paragraph 3 repeats:


  Note: This refers to the FFT processing core. As the Data In channel has a 16 element deep buffer on 
  its input, it can start to pre-buffer a frame while a frame is still being processed. In the case of 8 and 
  16 point FFTs, it can pre-buffer entire frames. However, this buffered data waits in the buffer until the 
  FFT engine has finished dealing with the current frame.


That whole section starting on page 52 provides a lot of additional information about buffering and flow control at the module interfaces. Why are you concluding that the data is not being processed correctly?