Those of us doing research have dead ended with John Tillman in South Carolina in 1782. All indications are though, the family (originally spelled Tilghman)came from the UK in the mid 1600's.
Note: about 20 years age there was a wonderfull documentary shown on public TV, and it reruns occasionally, by Ken Burns on the civil war. It had a picture of a Tillman Mercantile in Vicksburg MS at or about the time of the civil war. I've never been able to connect that to my line, but it sounds as it might fit yours. I've seen a better pic than this link, but it may be of help http://www.oldcourthouse.org/phototour.htm