My mistake. I was a bit tired. I have a M-Audio Delta 1010LT sound card.

For me, the problem is clear now. Melodist creates humanized tracks and it is not an error. Maybe I shouldn't make a big deal about that. RealTracks and Super tracks have the same, because they are played by humans.

Same for downloading other midi files to my daw. Some are humanized and some are quantized. And not an error in my daw or in a midi file.

Exporting chords from Biab was a different problem. Dan explained this (page 1). Default chord export is 40 ticks early. When I import chords with 40 ticks early, the import results are all 40 ticks early. So This causes a problem if I do not correct this. But this was also not a fault in Biab, but a setting I didn't know.

So I am very happy with the results here and I can move on.