Please help us out with more specific details. B.C. was not settled by Europeans until 1850's and later, so your Allen's from Scotland likely arrived in 1750's on the east coast of North America (eastern Canada, Nova Scotia, etc.) or American Colonies (Boston, NYC, Philadelphia, etc.) Remember the USA did not come into being until 1783.
Capt. James Cook did explore the areas around modern-day Vancouver and Victoria BC in the 1760's, mainly to survey and map the coastline, then he sailed off to his death in the South Pacific islands. BC started to be settled in those two cities by mid-1800's but growth did not take off until the long-promised railway connection to the rest of Canada finally arrived in 1885.
If you mean to say your Allen person actually settled in the 1750's in BC, he was truly a pioneer. The only way people could get there at that time would have been by ship going all around South America.