Tanning is melanin production in the skin. It does not necessarily damage the skin. In our safety studies on the 2nd generation copper peptides, melanin production was observed in the absence of sunlight. The safety of the copper peptide creams was tested by taping small plastic containers of the cream to the legs of paid volunteers for 5 days.
The manganese method may enhance tanning but looks likes like an oxidation of the skin's surface.