This might be what your hearing.
BIAB, in many of the styles has a setting to "push" a certain number of beats.
You'll find this setting in the Stylemaker, under the "Misc" menu selections.
There is a field for the "number of ticks to push" in that dialog. I suggest you set that to 0.
There is also a setting in the same dialog to "Allow Late Notes". Make sure that the checkbox is not checked on that screen so "late notes" will not be generated.

You might also turn off embillish for all patterns. I'm not sure if embellish introduces any "feel" effects, but it might. There is a setting under the "Style" menu in the stylemaker to "Set embellish for all piano/guitar parts". Put a zero in the box that pops up, and it will turn off embellish for all patterns.

My remarks are all in regard to the MIDI parts generated. Not realtracks.

Another option is to export to a MIDI file, then pull up that MIDI file in the DAW of your choice and quantize there.

Eric

... just one man's opinion ...