Winnie, here's what I have on Mr Joseph Alexander:
There may have been more than one Rev. Joseph Alexander in that area of SC in the 1770s, but surely the Presbyterian minister who served as pastor of Sugaw Creek P. C. in Charlotte, Mecklenburg Co. NC 1768-1772, where his uncle Hezekiah Alexander was a ruling elder, was the more famous.Later he served as pastor of Bullock Creek P. C. , York Co. SC, where he and his wife are buried.
He was the oldest son of Theophilus Alexander (1714-1768) and Catherine Wallace (c.1715-1775) of New Munster, Cecil Co. MD, and Theophilus was the oldest child of James the yeoman Alexander (1695-1779) and his first wife Margaret McKnitt (12.16.1693-c.1744).James in turn was the son of Joseph Alexander, one of the 7 Alexander brothers and 2 sisters who immigrated from Northern Ireland to Somerset and Cecil Counties MD.
The good reverend Joseph was born 3.15.1734/35 at New Munster and died 7.30.1809 at Bullock Creek SC.He graduated from the College of NJ (now Princeton University) in 1760.I don’t know what he did 1760-1767, but he had moved from MD to Charlotte by 1767, where he married Martha Davies (Davis?) on 11.12.1767.We have record of nine children: Martha “Patsy” b. 1768; Sarah b. c.1770; Samuel Davis (Davies?) b. 1771; Edith A. b.1774; Esther Davis (Davies?) b. c.1777; George Baldwin b. 1780; Judith b. c.1781; Ann b. c.1782; Margaret b. c.1784.
Joseph was ordained in 1768, and while pastor at Sugaw Creek helped found Queens College in Charlotte.He moved to York Co. SC after resigning at Sugaw Creek in 1772.Note that this is the period of the ferment which led to the American Revolution.He had the reputation of being a fiery patriot in York Co., and we are told some of his sermons are still available.
Union County SC, where the property on Tyger River is located, was part of 96 District in 1773.Union borders York Co. on the south, and Bullock Creek is in the SW corner of York Co.So while there is some distance between the Tyger River and Bullock Creek, it may have been that Joseph and his wife were living on the Tyger River in 1773 until he was called as pastor of Bullock Creek, where he lived out his days until his death in 1809.
One more note: In the late 1700s the American Presbyterian Church was basically a single denomination, north and south.It split into northern and southern branches in 1861 when our country itself split into warring sections.Hope this is helpful to you (and others).David