The "Fest der Jugend" was a Reich-wide event instituted in 1933 by Reich Minister of the Interior Wilhelm Frick to include normal schools, sports associations, Stahlhelmjugend, Bündische youth and other nationalist youth organisations (including the Hitler Youth - obviously). In 1933 it took place over the weekend of the 24th/25th of June to mark the period of the summer solstice celebration. Schools were closed on the Saturday and the central elements of the event on that day were sporting competitions. On Sunday the 25th there were hikes and rallies.
With the above in mind, these tinnies can't be seen as being exclusive to the Hitler Youth but could, of course, have been worn by many of its members.
Still looking for more info and will post as soon as I have anything more.