Powerll is only the chairman and basically spokesperson of the Fed. He however isn't making any interest rate decisions by himself and there is in fact a Board that votes on it. They base their decision on data and analysis fed to them by the staff under them at their respective Fed Banks.
The 7 members of the Board of Governors members aren't each individually associated with one or more of the 12 Federal Reserve Districts, that’s not how it works at all. There are seven members with staggered 14-year terms; three of those members serve as Chair, Vice Chair, and Vice Chair for Supervision, to which they are all appointed from the membership for four year terms, but aside from the three leadership positions and various committees that the boaed forms, the members all have general responsibility.