Bravo, your description is also correct.
Indeed, it was a major theme for Augustus, depicted several times on coins and carved on the statue of himself.
It was also very important because Mark Anthony and Julius Caesar both tried to reclaim the standards to the Parthians and failed. Succeeding even where Caesar failed was very important for Augustus. The recovery happened in 20 BC, only a few years after several important reforms so the new Princeps was in need of symbols and general support.
The coin with the black background is a depiction of the returned standard inside the Temple of Mars Ultor, over a triumphal chariot. This temple was built to commemorate the battle of Philippi and the revenge over Julius Caesar death. So it is amazing to see how this recovery has been integrated to Augustean propaganda.
This is why the lose of three standards in Germania by the defeat of Varus in the Teutoburg forest was worrying him so much. Two of them were recovered not long after but the last was recovered only in 40 AD.
Edit: Could someone gives a rep to Abdülmecid I? I cannot. Thx in advance.