the cities had a very large German majority (including Danzig) and had been under German rule for centuries.
Danzig is somewhat a special case in this. First, it was not part of the Reich between 1920 and 1938, but it was the Freie Stadt Danzig. The Freie Stadt found itself inside the customs territory of Poland, its monetary unit, the Danziger gulden was equal to the Polish zloty and the railway in Danzig was managed by the Polish state.
Before 1920, GdaĆsk became Prussian/German as a result of the second partition of Poland in 1793. In that year, the citizens of Danzig who were predominantly German were very unwilling to the Prussian rule, their preference being to continue to remain part of the Polish Commonwealth. So saying that Danzig was under German rule "for centuries" is a bit of exaggeration really.