They don't explain them by itself, they are just outside the scope of Bell's arguments since his assumptions are incompatible with multilocal hidden variables.How do "multilocal hidden variables" explain the EPR results?
The explanation of the nonclassical long-distance correlations is the standard quantum dynamics, which is assumed exact in the thermal interpretation and predicts the standard correlations. These are bilocal beables, approximately measurable (by the weak law of large numbers as any q-expectation; see Section 3 of Part II of my series of papers) through averaging over many independent realizations of discrete tests. The discrete response is explained by environment-induced randomness and environment-induced dissipation, as discussed in Subsections 4.3 and 5.1 of Part III.
The thermal interpretation does not give an explanation, though, of how Nature is able to figure out how to behave according to the quantum laws. It just follows them.