I don't know if you have ever managed an actual crisis situation, but I suspect not. So let me explain. You have a crisis called a world-wide pandemic. It's caused by a highly transmissible virus. That virus is present in your population.
So when a volcano erupts that puts life in danger, the correct response is not to shove everyone on cruise ships where there isn't space to socially distance (you might have noticed what happened on cruise ships just a short year ago?), or to evacuate them to islands that can't take them because they are struggling to get the virus under control themselves. Especially since refugee facilities on those islands will be non-existent, and the kinds of "facilities" available will increase rather than decrease the transmission and put everyone - refugees and local people - at greater risk.
So what you do is you contain the risk, managing that where, if the worst happens and it leads to a larger outbreak, you can better control transmission, medical resources and other services. And you encourage people to take up the vaccine as soon as they get there in order to start the process of reducing the risk, bearing in mind that it will take several weeks to substantially reduce that risk anyway, paving the way, if people do need further evacuation, for that to be done as safely as possible. Which is exactly what the Prime Minister is doing.
Eruptions are generally very manageable risks. You can relocate people out of the immediate risk area, but further evacuation at very short notice, if necessary (and it isn't often necessary) is generally easier to manage.
And yes, I used to to this sort of thing for a living. They are acting totally sensibly. Please don't use their situation to to illustrate a completely irrelevant comparison to the UK, vaccines and vaccine passports. I am fairly sure you will find that the only passport issues that the people of St Vincent have are very different ones than the ones you have.