In Caroline county, when you find the given name 'Spilsby/Spilsbe/Spilsbee', you look for a connection with the Coleman family. Originally, people with this surname appear to have come from the area around the town of Spilsby in Lincolnshire, England.
In America, the first appearance of the name of which I am aware in Virginia is where Robert Coleman (1656-1713) married Ann Spilsby (1659-1717), daughter of John Spilsby.There are many descendants of this couple, Colemans and allied families too, who gave their children the name of Spilsby or its variants.
Searching in the LDS and Rootsweb databases, I found that:
Spilsby Dyer was the son of James Dyer and Winifred Tribble, who was the sister of Spilsbe Tribble and the daughter of Shadrach B. Tribble and Elizabeth Coleman, who was the daughter of Spilsbe Coleman.
Which would seem to trace your Spilsby Dyer back to a Coleman as expected.