This is not quite acurate on the early Parchmans.Aquilla was actually a brother of Jesse and Philip was their father.James, John and Peter were also brothers of Jesse.
I am familar with the reference that I believe you are citing. As far as I know it's accurate from Jesse on down, but relied upon "old family stories" for the information before Jesse, which stories are often are a bit mixed up.
The Parchman family geneology starts with Nicolas, b. ca 1730.
He had three sons, Peter, ca. 1755, Phillip, ca 1758, and John, ca. 1770
Phillip had a very large family, John, ca 1785, Jesse, 1788, James, 1783, Sarah, 1795, Elizabeth, 1796, Permelia, 1798, Aquilla, 1800, Nancy 1802, Henry D, 1803, and Peter L. 1805
Phillip was originally from Pennsylvania, but most of his children were born in Tennessee.
Jesse and James are the brothers who went to Texas.Permilla and Elizabeth and their families did also.Jesse settled in North Texas near Marshall and most of the North Texas Parchman's are decended from him.Jame, Permilla and Elizabeth settled in Central Texas.
Quite a bit of information over 100 pages on the Phillip Parchman family that includes Jesse can be found in "Family Ties: The Parchman Family Tree", compiled by Kenneth R. Whitley, 1993.This book is available at the Texas State Library and Archives in Austin, TX.