Normann exhibited in Oslo, Berlin, London, Vienna, Düsseldorf, Munich and Paris. Although based in Germany from 1883, he would return to Norway each summer. Normann and Hans Dahl both had large ornamented wooden villas near Balestrand where they would entertain. His "dragon style" house was bought in 1891 and built (like many Norwegian houses) from a pre-fabricated kit from the city of Trondheim. The house stayed with his heirs until 1934.
Normann notably exhibited at the prestigious Salon de Paris from as early as 1882. His paintings earned a Mention Honorable in 1884 and he was awarded a bronze medal in 1889. It is assumed that his fjord paintings contributed to make the Norwegian fjords a popular tourist destination.