...so had the Germans broken the Italian codes and were just waiting for the official announcement or did they really get organized that fast the night of 8 September and morning of 9 September.
Yes, it appears they had broken one of the Italian diplomatic codes. There may have been information from Italian leaders or others still loyal to Mussolini or the Axis in general. While most Italians were sick of the war there were more than a few who thought the capitulation was a shabby betrayal. It is quite possible more than one was passing information to the Germans. I'm unsure when the Germans understood the Italians were negotiating surrender, but they seem to have known the content of the messages between Rome and the representatives before the agreement was reached.
Siegfried Knappe was a artillery officer with a German infantry division in Italy. In his auto biography he described how the division staff planned a decaptation of the nearby Italian inf division at least 48 hours before the surrender announcement. Historians of the Italian campaign like WGF Jackson describe how the movement of German ground forces into Italy was accelerated 48-72 hours before the announcement.
Many Italians expected a large landing on the coast near Rome, & the leaders of the Army HQ defending Rome had been planning with the US a airborne drop on Romes airfields. When the airborne op was canceled & the amphib action did not occur the morale of the Rome garrison went from bad to terrible. Those divisions were among the most reliable Italy had remaining and most surrendered or deserted when the Germans attacked them. Elsewhere the desertion rate exceeded 50% in the 48 hours following the surrender announcement. This suggests whatever plan was in place, or might have been made would fail anyway as only a small percent of officers and soldiers were willing to fight.