No, I don’t think evolution has to do anything with stress on vaccination these days. Other species of animals, coming under the humans in the evolution tree, live life given by god as it is. They live till they are healthy, die when become sick. They can’t apply brains to increase their life span by battling diseases.
Humans on the other hand have very sharp brains, that is why we are highest in the evolution ladder. We are going as per the evolution, first we discovered the unknown diseases and their causative agents. Then our scientists invented cure of diseases. The most important invention, which had a direct effect on increasing the life span of humans, was the discovery of vaccines. After which, we were able to control epidemics and mass deaths of children and adults significantly. The global average life expectancy has increased more than double than what it was in 1700. Infant and child mortality was high in ancient times than today. Many thanks to vaccines for it.