Yes, I see Thomas Harber in 1850 in Nicholas County, age 58, born in VA. Next door is a David Harber, age 38, born in KY. So that seems to put this family in KY before 1812. Sure enough there is a Thomas Harber in Nicholas County in 1820 and 1830 census.
Robertson County was formed in 1867 from parts of Nicholas, Mason and Bracken. I note that your Luke Harber lived in Mason in 1850 and 1860, but Robertson in 1870 and later. He may not have moved at all. It may be that the new county formed in the area where he already lived.
There is a case in New Jersey that I knew of where three members of the same family were all born in the same house -- but in three different townships and in three different counties!
Keeping track of all these changes while you are researching is a challenge. Also, the way people answer the birth place question in census records may vary from family to family. If a person was born in what is now Kentucky before 1792, he might say that he was born in Kentucky, or he might say that he was born in Virginia. And just to throw something else in the game: up until 1863, Virginia included all of what is West Virginia now.
There are several kinds of historical maps online. One is here:http://publications.newberry.org/ahcbp/
Click on your state. The first selection for each state, interactive map, lets you see what the counties were for particular dates.
Another comment: Thos is a common abbreviation for Thomas. Other common abbreviations are Jas for James, Wm for William and Jno for John. (Don't ask me why people would abbreviate a four-letter name with an incomprehensible 3-letter abbreviation.) Ancestry doesn't handle these abbreviations very well. When searching for Thomas or James, use wild cards: Tho*s and Ja*s. For William and John, you may have to search for several possibilities -- or leave out the first name entirely if you can. FamilySearch seems to handle these abbreviations and variations better, so you could search there too.
America Robinson might have been a worker of some sort, or a boarder, or a relative. I try to identify miscellaneous people in each household when I can -- unless they are clearly just boarders. About half the time the "miscellaneous person" turns out to be some relative: wife's sister, somebody's niece, etc.
I think you are on the right track, looking at all those Harbers in Mason, Nicholas, Bracken, etc. area. You may be putting together a pretty sizeable family tree to get everybody sorted out. I suggest that you do this on Ancestry, so you can attach the records you find.