What if she was on a mission and neeeded a long-term cover? Maybe she used him as a way to investigate ties between the Irish and the Yakuza to check on the Hand. Perhaps they purposely pick strong fighters as better breeding stock or something and Jack fit the bill genes-wise. Or she had a one-night stand with him and she decided to dump Matt on him rather than raise him herself. Possibly she was a supporter while not being a member and called Stick in to train her estranged son, etc.

Take the basic concept and run with it. Do whatever you want, go nuts, and have fun with it!