> A slower spreading virus would produce more mutations over time

Mutation is not primarily a function of time but of infections. So mutation is higher when there are more hosts. Letting the virus infect people leads to more mutations.

Now we're probably not talking about the same thing when we say mutations. I mean the sum-total of mutations. You mean successful mutations. But here comes the connection: The virus is more likely to evolve into infecting vaccinated people when it is more widespread. Because there are more mutations and consequently more chances for one of them to evade the immune response of vaccinated people.