This is in Tallahatchie County MS
Info from the site you linked:
Facility Type: male Maximum-security CCA owned facility since Mar-00
Total Beds: 1,104
Customer Base: Tallahatchie County (County Jail) and the states of Mississippi and Hawaii (and now California).
About Tutwiler: Tallahatchie County Correctional Center is located one and a half miles north of the city of Tutwiler on U.S. Highway 49 and occupies approximately 27 acres of the 149-acre site.
Tutwiler, MS is a rural farming community with a population of about 1,800. It is noted to be where “Blues Begin.” The current Mayor is Robert Grayson.
Tennessee has been housing California inmates for some time. I don’t know their legal status though. Maybe their trying to break up the prison gangs out there.