They do. Medium wealth workers do work medium wealth jobs.
What is not the case though is that medium wealth properties only contain medium wealth jobs/goods. Residents do fit this bill and medium wealth properties will provide medium wealth workers. But industry and commerce buildings run the gambit of jobs they offer, not just one or the other.
For a more detailed break down of what type of buildings offer jobs for what wealth levels take a peek at this question here: What type of buildings offer what level of jobs?.