Yes, the parents are Capt. Henderson Madison (or Matthew) Walsh and Evelina C. (Harrison) Walsh.Yes, they are from Neshoba County, MS.
The parents of "The Captain" are Jonathan & Winnaford / Winnyfred (Kirby) Walsh.This Jonathan Walsh had a brother named John L. Walsh . . . just want to clear any confusion regarning the names Jonathan & John from the same family.
Jonathan Walsh's parents are Thomas & Elizabeth (Benton) Walsh.
Thomas' parents are Thomas Walsh Sr. and Margaret Madison (McGinnis) Walsh.This middle name of "Madison" is why I speculate that "The Captain's" middle name may be "Madison" and not "Matthew" as is the name of his son, Henderson Matthew "Matt" Walsh.
More information is that Evelina C. (Harrison) Walsh's name is spelled "Effelina" on the 1880 Census and she is living with her son, Hugh H. Walsh in Hood County, TX.