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Due to the mis-matched mesh, you should get better results by setting INIPENE=3, then applying the OFFSET manually.
Note that if you are really interested in detailed stresses due to this press fit, you should really refine the mesh. This will not only give you better contact results, but your pin should have at least 3 elements through the thickness for good internal stress results. One element through the thickness is not sufficient.
If you are simply trying to model gross stiffness and load transfer in this joint as part of a much larger overall structure, then this mesh density and either contact approach is probably sufficient.
OFFSET can be specified: