Nathaniel Charles Alston of Stewart County was the son of John Alston of NC and Charity Tate of Elbert County, GA. John Alston was the son of James Alston, Jr of Chowan County, NC and Grizell Yancey of Granville Co NC. James was the son of James Alston and Christian Lillington of NC. Nathaniel lived in Gainesville, GA and Enon, AL prior to moving to Stewart Co GA. One of his brothers, John Theodore Alston, lived in Webster county GA. The reminder of his siblings lived mainly in Monroe County GA.
Joshua, Susan and Cyrus Alston do not connect to the Nathaniel Alston family based on my research. So I believe that your assumption is correct regarding a connection between the families.