Not seeing the effects of action on a vector's last element via a reference

It seems I don't fully understand how exactly C++ references work. Trying to run following snippet:

std::vector<int> test{1,2,3};

int& ref = test.back();

auto lambda = [&ref, &test](){
  std::cout << "inside lambda " << ref << std::endl;  
  ref += 1;
   for (auto&v : test)
   std::cout << v << " ";
};


lambda();
lambda();
lambda();
test.push_back(5);
lambda();
lambda();
lambda();

return 0;

}

And got this result:

inside lambda 3                                                                                                                                                                       
1 2 4                                                                                                                                                                                 
inside lambda 4                                                                                                                                                                       
1 2 5                                                                                                                                                                                 
inside lambda 5                                                                                                                                                                       
1 2 6                                                                                                                                                                                 
inside lambda 6                                                                                                                                                                       
1 2 6 5                                                                                                                                                                               
inside lambda 7                                                                                                                                                                       
1 2 6 5                                                                                                                                                                               
inside lambda 8                                                                                                                                                                       
1 2 6 5  

Why after push_back is done, none of vector elements is incremented? And where ref points to from this moment?