In 1881 census, Thomas says he's born Ford Mills. So I think the 1851 census at Ford Mills is correct. Brother John says he's born Alwinton, further down the page is a James Nesbit also born Alwinton.
This is likely to be them in 1841, transcribed as Nistit on you know what.
Ford Mills, Ford, Northumberland,
Ann Nesbit, 50, Y, Independant,
Ann ", 20, Y, Dress Maker,
John ", 20, Y, Blacksmith,
Margaret ", 20, Y, Dress Maker,
George ", 15, Y, ? Man,
James ", 15, Y, Blacksmith,
Thomas ", 11, Y.
HO107/833/16/5/2
There is a burial of a James Nesbit of Ford Mills, age 56, 10 August 1839 at Ford St. Michael.
Hope this link works, needs checking out, but can't see anything obvious to contradict it.
http://www.sfu.ca/~jcnesbit/gen/NesbitFordForge/Alan.