Well guys and gals, I solved the problem by myself.
Actually the problem is not in the tray mechanism itself, but it is in the plastic round of the top cover of the burner.
It has, inside it, a little circular piece of metal that is useful to let the motor hook the disc: when a disc is inserted, the tray mechanism goes up and the motor too. The motor has a magnet in itself and it attracts the metal piece inside the plastic round. The disc is kept in between of the two attracting pieces.
The problem, in my case with the DVR-216 is that the magnet is attracting the piece of metal in the plastic round really hard and the tray motor wasn’t able to do enough force to let the magnet and the round of plastic unhook.
My solution consisted in remove the label on the top cover of the burner. This way you can unscrew the top plastic cover protecting the plastic round and then remove the whole plastic round.
You can see the metal plate in it. I just changed a bit the orientation of the metal plate to let it make less attraction with the magnet of the motor. Be careful because the metal plate is a bit hard to remove from the plastic round. I had to break the three little plastic hooks in the middle and then two of three peripheral hooks to turn it, remove it and then reinstall it a bit pulled up on a side.
Do not think to remove the metal plate: the disc won’t be kept in the right position and it won’t spin at all.