Auto function in the case of the 109E came in to general operational use in late 1940. The earliest reference I have seen is Sep 18 1940 when it was being tested in a machine of II/JG53. The 109E in the RAF museum Hendon was Field Modded to AUTO it is an E3B I believe. It was brought down on 27 Nov 1940. Steinhilper's book "A Spitfire on my tail" refers specifically to Manual prop pitch technique still being used as late as Sept 1940. There is a translated OKL document discussing the introduction of AUTO on the 109E its subject header is "Increasing the revs of engine types DB601A and DB601N. It is hand dated 14Th Nov 1940.
Here is an image of the translated document :
