Dear Ms. Davis -
The only clear connection I can find in Hewett is between Nathan T. Davis, Co I, 12th Texas Infantry, and H. O. Davis, 12th Texas Infantry, Co I. I have no idea if this unit was near Tyler (Smith County) Texas in August 1862, but units deploying to Arkansas were passing through the county, since General H. E. McCulloch was headquartered there.

You can get their service records from the H. B. Simpson research center at Hill College, Hillsboro, TX.