I've reviewed my notes on this Alberson branch. Solomon Alberson/Albertson (the spelling fluctuated) was born 1754; he was the son of John Albertson and Elizabeth Early. He had a brother Early born 1756, and a sister Ann.
Solomon had son Early and Moses. Their census records are:
Solomon: 1790, 1800 and 1810 in Pitt, NC; 1820 in Wayne, TN
Early: 1800 in Pitt as Yerley, 1820 in Wayne, TN; 1840 in Lafayette co, MO; 1850 and 1860 in Miller co, MO
Moses: 1830 and 1840 in Wayne, TN; 1850 and 1860 in Perry, but probably did not move. Rather, when Perry was created from Wayne, Moses was in the "Perry" part
The composition of Moses' household shows a male 0-10 in 1830 and 10-15 in 1840. This was probably the John that you mention, who was 30 in the 1860 Census.
Early (1780) moved to Lafayette; one of his sons, Solomon born 1819, moved with his family to Oregon by 1850. This branch of the family is well documented.