Why Taxes are due on 30.9. in ZH?

This is what the city of Zurich says: Definitive Rechnung / Schlussrechnung - Stadt Zürich

Seems in line with what you state.

BTW, people were already confused back then when Switzerland moved to Gegenwartsbesteuerung back in the early 2000s (Zurich apparently already switched in 1999).

Here’s the corresponding NZZ article from March 2002: Die Konfusion mit den Steuern | NZZ

The 1% interest you owe (get paid) today was 2% back then.