Quantization can be a good thing to correct mistakes in timing, but can also be a bad thing in that it kills the natural flow of a style and adds a robotic feel (just think of the Yamaha styles: they are all over-quantized).
Anyway, since the Audya apparently doesn't offer a complete style edit mode but only a style remix feature, you need to export all the parts of a style to a sequencer (in .mid format) and then use the quantize function of the sequencer itself; there you can choose the amount of quantization (1/4, 1/8, 1/16, 1/32, triplets, ecc). My advice would be to use the lowest amount possible, like 1/32 of a note, to avoid huge note shifting; you have to try and listen to the result until you are satisfied. Then you can import the midi sequence back to the Audya in style (pat) format; a program like Styleworks can do this conversion process very quickly. Hope this helps.
Good luck.