Hitler and the Nazis believed in a nation for all the German people, which included Austria. Austria was actually annexed by Germany in 1938. So Hitler being from Austria wasn't a big deal. He even fought in the German Army, not the Austro-Hungarian Army, during World War 1

This is the first paragraph of Mein Kampf

I consider it my good fortune that Fate designated Braunau on the Inn as the place of my birth. For this small town is situated on the border between those two German States, the reunion of which seems, at least to us of the younger generation, a task to be furthered by any means necessary.

German-Austria must return to the great German motherland, and not because of economic considerations of any sort. No, no: even if from the economic point of view this union were unimportant, indeed, if it were harmful, it ought nevertheless to be brought about. Common blood belongs in a common Reich. As long as the German nation is unable even to band together its own children in one common State, it has no moral right to think of colonization as one of its political aims. Only when the boundaries of the Reich include even the last German, only when it is no longer possible to assure him of daily bread inside them, does there arise, out of the distress of the nation, the moral right to acquire foreign soil and territory. The sword is then the plow, and from the tears of war there grows the daily bread for generations to come. Therefore, this little town on the border appears to me the symbol of a great task.

So far from hiding it, Pan-Germanism was the basis of Hitler's ideology and political program. In fact Austria even had its own fascist movement, led by Engelbert Dolfuss, that took power before the anschluss. Compared to the Nazis the Austrian fascists were less violently anti-semitic and more pro-Catholic. Dolfuss was assassinated by the Nazis because his fascism would have preserved an independent Austria. Mussolini preferred Dolfuss to Hitler and was very displeased when Dolfuss was assassinated, not that there was anything he could do about it.

At this point of time, Austria, is just more or less another South German culture, like Bavaria. Culture was markedly different, than from say East Prussia, but this is also true for Bavaria. Both were considered part of the German nation. They were "Volksdeutsche", just like Sudetendeutsche in Czech Republic. Part of the same nation but living in a different state.

Austrian people, as a somewhat different ethnicity from Germany only evolved after World War 2, and was long contested, even somewhat today.