That was the patch I was looking for! Now everything is (almost) working. I stumbled upon another strange problem:
if I use the oscillator integrated on the evaluation board, to generate the MCLK, everything works as espected; if I use an external signal (with the same 12.288Mhz frequency, verified with a scope) as MCLK, it works as long as I don't use the DSP.
What am I doing wrong?