I talked to my father and he said the only restrictions that he knew of were that the instructor must of course pass interviews with both US Aviation and American Eagle. After that they just have to meet ATP requirements.

Instructors could transfer into US Aviation with hours; they do not have to be new instructors as far as he knew. There was also no required amount of time that they must be at US Aviation that he knew of.

However, on a personal note, I would be skeptical of US Aviation's willingness to hire an instructor who was only planning to stay a month or something. You can apply to American Eagle outside of US Aviation. It is just a great perk to have all their benefits while being a CFI.