The first use of the term "Nazi" by the National Socialists occurred in 1926 in a publication by Joseph Goebbels called Der Nazi-Sozi ["The Nazi-Sozi"]. In Goebbels' pamphlet, the word "Nazi" only appears when linked with the word "Sozi" as an abbreviation of "National Socialism".
After the NSDAP's rise to power in the 1930s, the use of the term "Nazi" by itself or in terms such as "Nazi Germany", "Nazi regime", and so on was popularised by German exiles outside the country, but not in Germany.
The Gestapo and SS were organs carrying out Nazi policy. Nazi members were in Holland and elsewhere making the public statements about how people were to behave and what minorities were to report for transport and reeducation, etc.
The timeline here works.