David Hackett Fischer's book “PAUL REVERE'S RIDE” lists 100-150 people who were part of the Boston Tea Party. One of those listed is a Joseph Payson.
For your info, many of the settlers in NS during the 1750's and 1760's (there was no New Brunswick until 1785) were given grants of land there by the British, who had taken over the old French lands known as Acadie (Acadia). Acadie since the early 1600's had included what is now NS, NB, and parts of Maine and Québec to the mouth of the St Lawrence River.
When the English destroyed the French fortress of Louisbourg in the late 1740's and moved their capital city from Annapolis Royal NS to Halifax in 1749, they encouraged anyone who was (first) Protestant and (second) non-French to settle in what had been the old Acadie. Ironically, many settlers at this time were French Protestants (Huguenots) who were settled in England and Ireland since the 1600's and were encouraged to take land in the New World.
Part of this policy involved the deportation of 1000's of Acadiens from the Annapolis Valley starting in 1755. These people were rounded up by Gov. Lawrence, put on boats, and forced to sail to the USA, Québec, and even France. Those who settled in Louisiana were called "Cajun" after the old name "Acadien". English or other settlers were then given their lands in NS.
It is very likely that the Payson and other English colonialists were looking for new lands to settle, since the Eastern US was becoming crowded by the 1750's (none of the territory west of the Mississippi was opened up yet, and only a little of the Ohio River Valley). This is likely why they made the move.
When they found the land in NS (as we know it now) was largely unsuitable for large-scale farming, they went to the Saint John River Valley in (what was to become) NB. These people faced a lot of adversity, including blazing summer heat (high 90's F.) and long bitter cold winters (-40 F.). Just as they were settled into their new lives, and the second generation were starting to run the farms in the 1780's, tens of thousands of Loyalists who were fleeing the Revolution arrived all at once, with little or no planning how they would be accomodated before the next winter set in. There was a lot of chaos and resentment against the newcomers, and against the English military who had dumped them in NB and NS (New Brunswick became a separate province from NS in 1785).
It is likely that some of the early settlers of 1750-1770 (often called Planters) were upset enough to move again, perhaps to the USA, or often westward to Ontario or the Eastern Townships of Québec. Quite a number of these people later migrated back into the USA. Up to 1 million Eastern Townshippers and French-speaking Québeckers moved to New England from 1860-1960, to work in textile mills and moving logs on rivers. The people in Southern Ontario often moved south and west into IL, IN, MI, MN, WI, and from there they fanned out into the rest of the USA.