"...herd immunity - at least in the most common understanding - is not about how likely a disease is brought to the herd."
One critical factor to herd immunity is that of vector. Immunized herd members are reckoned unable to transmit the disease. Therefore, adding a substantial attack vector of potentially infected persons to the 'edge' of the herd, as happens with tourists, directly impacts herd immunity negatively.
"...why should not being check for vaccination automaticly put you out of the herd?"
Granted. I was incorrect. Thanks for pointing it out.
"The concept doesn't care about who you are and where you are from. It only cares about how many of the indivduals being there are at that time are immune and how many are not."
This is why the tourists aren't part of the herd. Since they are only temporarily present, they do not contribute - other than as potential vectors of infection of the herd - to epidemic.
Thanks for your substantive reply!