By a wonderful coincidence last night I was looking for a lead on a Francis Tibbetts (or Tibbet), who according to the family traditions was in Allen County, Kansas Territory in 1860. In the 1860 US Census for Allen County I came upon an Isaac W. Tibbet (sic) in household 359, b. abt 1812 in Maine, with a son Isaac born 1839 in Indiana living with him, and an apparent son Benjamin, born about 1835, also in Indiana, living next door with wife and daughter. The older Isaac's wife was Susannah, born about 1810 in Ohio. (Unfortunately did not find a Francis.)
My normal resources for Tibbetts data do not have these folks. With so many apparent matches, are they possibly related to the Isaac in your query?