 The MWI does not have action at a distance. The most celebrated example of nonlocality of quantum mechanics given by  Bell’s theorem  in the context of the  Einstein-Podolsky-Rosen argument  cannot get off the ground in the framework of the MWI because it requires a single outcome of a quantum experiment, see the discussion in Bacciagaluppi 2002, Brown and Timpson 2016. Although the MWI removes the most bothersome aspect of nonlocality, action at a distance, the other aspect of quantum nonlocality, the nonseparability of remote objects manifested in entanglement, is still there. A “world” is a nonlocal concept. This explains why we observe nonlocal correlations in a particular world.