I just bought a pair of M22 ti's and they sound great. Now I'm thinking of getting a subwoofer. I have an Adcom stereo amp. On the axiom web page it says to run the speaker cables from the amp to the subwoofer in, then run them out to your speakers. This may be a stupid question, but, does that mean the amp in the subwoofer is powering the bookshelf speakers?

No, the sub is simply taking the signal and applying it to its own amplifier. It does not draw any power from your amp (well maybe a few mv). Usually this setup doesnt sound as good as if you took a preamp output and ran in into the subs rca inputs but if your amp doesnt have those outputs the speaker wire way is what you'll have to do.