Did John Q. Adams have any clue, for example, that Andrew Jackson was going to beat him before the actual election results came in?
I think that the 1824 election was conducted more like a party nominating process than a final election. All the candidates were from the same party. There were electors who voted for Adams for President and Jackson for Vice President, and of course Calhoun was overwhelmingly elected Vice President. Jackson got a majority of the EV from two states where he was beaten in the popular vote.
It was probably a reconstruction after the fact to make a big deal about the popular vote, since Jackson believed that Clay did him in in the House.