This might be a late reply, but I too received the revised admission reply form.
Mine is a little bit different from yours because it does not specify where to work. Perhaps, it's because I'm international?
"In addition, the department is offering you the option of working with any Politics faculty member on a project of mutual interest for which you would be paid an hourly wage up to $2,000 over your first two years."
I'm worried about working in the first year, so I think I'd rather decline this offer if it's possible.
I should ask some grad students at the visit days about this offer.