Then, how do you know the local business owner isn't, in turn, using that profit to buy stuff from companies with directors and shareholders sitting on beaches in French Polynesia?

If you track the individual dollars, most flows of value eventually, after some number of loops, end up with the French Polynesia sitting people.

That local business owner pays taxes and presumably eats food and uses services from his or her own town. They also pay local people to work in their shop who also presumably spends some of their wages locally.