My son is preparing for grade 3 violin and has been trying to play along with the recordings of the pieces. We've started using speedshifter to slow down the tempi, and he has really enjoyed playing along to an easier speed. Yesterday we suddenly noticed that the tempi he is now playing the pieces at are almost identical to those marked on the music, but much slower than on the recorded tracks.

So which is correct? some of them differ by almost 20 metronome marks, which is a big difference in my opinion.

There's no 'correct' tempo, whether for exam or for any other performance. Tempo marking are a guide - and in exam books, they're often editorial suggestions (look for the square brackets) and prefaced with 'ca.'.

You're free to take as much liberty with your choice of tempo as the performer on the recording did, provided it still captures the right mood for the piece.