Activating the quest can be done through several means. Completing the main story line quests of any other faction (the NCR, Mr. House or Yes Man) can activate it, as can gaining infamy with the Legion after receiving the Mark of Caesar. In the former case, the quest will activate as a warning. Completing one more mission will cause it to fail. If triggered by Legion infamy, it will activate and fail on the spot. It will only activate after having cleared of Legion infamy (if applicable) following the completion of Ring-a-Ding-Ding!, or after dealing with the Great Khans during For the Republic, Part 2 as siding with the NCR does not require confronting Benny.
Once failed, the Courier's reputation with Caesar's Legion will immediately turn negative, which in turn may cause the appearance of Legionary assassins by triggering Caesar's Foe. The Courier is also proclaimed "in damnatio memoriae" (condemned in memory).
This quest could be described as a counter quest to Don't Tread on the Bear!, even though it is possible to trigger both at once without actually failing either.
Its possible to activate Beware the Wrath of Caesar! by not confronting Benny at the Tops but still advancing through For the Republic, Part 2.
It's also possible to trigger this quest by releasing Benny during Render Unto Caesar, which will immediately drop your reputation with the Legion to vilified.
It's possible to prevent the appearance of Legionary assassins when failing this quest, by raising the Courier's reputation with Caesar's Legion to Idolized beforehand (by delivering enough NCR dogtags to Aurelius of Phoenix or Severus). The reputation will then be changed to Wild Child when failing the quest, reputation not negative enough to make the assassins appear.
"Damnatio memoriae" is the Latin phrase literally meaning "condemnation of memory" in the sense of a judgment that a person must not be remembered. It was a form of dishonor that could be passed by the Roman Senate upon traitors or others who brought discredit to the Roman State in which the condemned are erased from history.