I believe "your" James was born about 1835 in Glasgow, Scotland and is probably the son of John and Agnes (nee SULFERAGE). There is a likely brother George and a sister Elizabeth. I can prove James died in 1892 near Manchester in Lancashire, England. He had 10 children and they all lived in the Manchester area. One child was called Janet McBrayne TIBBETTS, interesting because of George's wife was Janet McBRAYNE. George had only one son, John. John lived briefly in the Manchester area, but seems to have returned to Glasgow, dying there in 1913.
I have also researched Lawrence TIBBETT's ancestry, which goes back to the TIBBITS of NY, who probably all go back to the Rhode Island TIBBITS.
Nearly all TIBBETS (whatever the spelling) in the US are all related, but you have to go back to prior to 1635, and to Warwickshire, England to find the links.
If you can explain yor link to James, may have more info to help.