This is quite interesting and I don't have an answer so I'm wondering. Some names of my ancestors who migrated from the Southold area to Orange county (NY) are:
Watkins, Booth, Ackerly, Horton, Conklin, Hawkins, Harlow, Satterly, Goldsmith, and Tuthill.
All of the migrations appear to happen from the 1730s through to the early 1770s then stopped abruptly just before the Revolution. About the only ancestors who stayed (relatively) put were the Gardiners. I might also suggest that if you're researching any of these families and have reached a dead-end to check the Orange county New York records.
Why they would leave the Southold area? One note I have regarding Timothy Hawkins (b. aft. 1712) says, "In 1772 went to New York Samuel Walker, Jacob and Isaac Slaughter, Moses and Timothy Hawkins." By, "New York," the note refers to Orange county.
Is this a case of younger sons who might not ordinarily inherit much striking off on their own? Could it be the change of government from Connecticut to New York? I don't think it was anything having to do with revolutionary sympathies as both Suffolk and Orange were, largely, patriot in leaning.