There are two marriages attributed to Jemima Hulse, at the same time and place - both In 1733/4 (early 1734) - both in Southold.
John Case m. Jemimia Hulse - in 1733/4 (Wrong)
John Overton m. Jemima Hulse - on 1/1/1733/4 (Correct)
Charles Moore's Town Of Southold - Index of 1698 on page 64 - it says:
110. Case, John prob. son of 106, p [died] 6 Feb 1775 age 57: he or a namesake m, Jemima Hulse 1733/4.
on page 106 - it says:
502. Overton. Isaac, prob. son of 'Isaac, B. 1683, D. 4 Nov., 1723, .£. 40h; m. Abigail, dau. of '-Nathaniel Moore, No. 463; c, prob. Nathaniel, who m. Alathea Way in 1732 (Index of 1775)—John, who m. Jemima Hulse in 1734 (Index of 1775)—James, who M. Mary Goldsmith in 1745.
The Salmon records on page 83 [p. 129 - Marriages] - it says:
1733/4 Jan 1 - Jn Overton & Jemimah Hulse. on page 96 [p. 144 - Marriages] - it says: 1760 July 9 - John Case & hannah eldrydg. [actually Hannah Aldrich]
There is another marriage of John Overton and Jemima Hulse, about 1775 - These two are cousins.
This second John Overton is son of David Overton and Anne Hulse - who is sister of first Jemima Hulse.This second Jemima Hulse was daughter of John Thomas Hulse - who is brother of ftrst Jemima Hulse.
No wonder there is confusion about this mystery - Solved!