Only watch Amazing Race.
I think the cameraman follows one team around. Its impossible to
have different cameramen at different countries. I suppose a pair
of cameramen is in charge of one team and they take turns to film,
like for example, Cameraman A film for day 1, Cameraman B will film
on day 2 and so on. They may change shifts every 2 days or
something.
Kinda tiring to carry a huge camera around and run with the
contestants... Tough job for the editor too...