OK, after the 2nd viewing, I’ve further refined the theories. 1st, the part about the TV screens being predictions of Neo’s behaviour…bingo.
Second, I now believe that the world of Zion is in fact real and that Neo has learned to control the machines from there. Not sure exactly how (802.11a?) but remember that when Neo destroyed Smith part of Neo got imprinted on Smith. Perhaps part of Smith got imprinted on Neo then or when Smith tried to clone himself to Neo. Remember that the agents do have access to the Matrix mainframe and control of the Sentinels.