I know of no Jones ancestry for either John T. Williams or Phoebe Ferguson. It is quite possible that he was named after Ambrose Jones Sr. (1756-1833) simply because of the prominence of that gentleman as one of the founders of Morgan Co. in 1823, as was John T. Williams.

Morgan Co. marriage records list the marriage of Ambrose Williams and Anna Hill on 25 Mar 1847 by W. W. Brown.

(The minister, William Wallace Brown, was married to Anna’s sister Nancy.)

1850 census of Morgan Co., Ky, enumerated 26 Aug, lists on p. 66 as family #423:
Ambros Williams, 23, farmer; Anna, 22; William, 2; John, 11/12. All born in Ky.

1860 census of Morgan Co., Ky, enumerated 20 June, lists on p. 31 as family #191/189:
Ambrise J. Williams, 33, farmer; Anna, 31; William W., 12; John E., 10; Amanda M., 8; Leander J., 5; Sarrah C., 3; Susan C., 9/12. All born in Ky.

1870 census of Morgan Co., Ky, River precinct, enumerated 7 July, lists on p. 7 as family #45:
Williams, Ambrose J., 43, farmer; Anna, 43; William W., 22; John E., 20; Amanda M., 18; Leander, 15; Sarah, 13; Susan C., 10; Martha A., 7. All born in Ky.