How does the MMR vaccine affect lymph nodes in preventing measles?
Lets define viremia first: The primary viremia occurs in the cells which the virus enters first in the body. There it replicates to high titers before it leaves this cells, spreads through the body and infects other cells. This is then the second viremia.

For measles the primary viremia occurs in the respiratory epithelium and in the local lymph nodes. The second viremia then occurs in skin, conjunctiva, respiratory tract, and other distant organs. In this phase also the characteristic rash occurs due to a hypersensitivity reaction of the skin. For details see here and here.

The measles vaccine works like any other vaccine: By raising an immune response against the vaccination virus. This leads to a normal immune response which leads to the production of specific antibodies against the measles virus and also to immunologic memory. These antibodies are available to fight the virus when it enters the body of a vaccinated person. This also triggers the proliferation of virus specific memory B cells which then differentiate into plasma cells and produce vast amounts of protective antibodies. So there is no special mechanism involved here beyond immunologic memory.