That said, I don't think there's necessarily a correlation between low axis rotation and matching up (or not) to asymmetric cores. Similarly for tilt. Most asymmetric-cored balls tend to give more length and backend than similar symmetric-cored balls (so far as there are "similar balls"), someone with a lot of tilt already has length and backend built into his release. An asymmetric core might help if he really needs the kind of reaction that combining those two things would give. Or it might hurt, if he needs a rollier, smoother ball motion. The low tilt, low rotation guy might like that length and backend to generate more angle
Now, you'll get plenty of responses saying "well I've got lots of tilt and side rotation and my Asyminator 9000 works great" and just as many "I track high and have very low tilt, but I can't throw a symmetric ball and carry the 10-pin for nothin'".
The only thing I would say for sure is that layout can really make or break a strong asym. The wrong layout or the right layout on the wrong condition can really make a big difference between a great ball and one that just doesn't react or carry like you want.
SH