You don't agree with this statement? I presume since the "Apparently haha" comment. However, I agree; there was definitely a distinct imperialisitic nature that was instilled into the towns of Pompeii and Herculaneum as a result of power in Imperial Rome. For some reason, the structure of that question is giving me mind spins; but I'm not sure if the fact that it's Friday afternoon and I haven't had coffee today if that's what is causing the confusion.
Okay, so of course public buildings, social stratification, political constitution and architectural designs all portray how Imperialistic power infiltrated the towns of Pompeii and Herculaneum. I'll give you a couple of examples that I can remember off the top of my head (so be sure to double check facts, information and dates that I provide).
In terms of architecture the inclusion of an Atrium and Peristyle designed house places huge emphasises on the Imperial Roman Period as that was the common features in Imperial Rome; which thus shows the dominating concept of Imperialism as it even impacted on how houses were designed in provincial towns throughout Italy, far the from centre of Rome itself. You might also want to note that during the Imperial period many houses were replaced by public religious buildings and shrines, thus again showing it's influence on the construction and development of the towns. Also, important to mention would be the Public Temple of the Lares - which are argued as housing statues corresponding to the Imperial Family. Also the fact that the Temple of the Genius of Augustus / Vespasian were built; demonstrates Imperialistic power over the towns, and the importance these individuals as they were displayed throughout the sites. The Forum also shows influence of Imperialism; as evident from the changing of public buildings (Temple of Vespasian, statues) and the dedications by public donors (such as Mamia) which portrays the influence and importance of imperial family members wanting to gain popularity in the provinces. The statues and dedications discovered also portray how individuals proceeded to gain political importance, similar to that of Imperialistic methods.
In terms of social stratification and features to prove Imperialistic power, you could mention that with the Genius of Augustus / the Imperial cult that developed during the time of Augustus the social norm was to believe that rulers were descendants from the Gods, and that society worshipped the divinity of the Emperor; which was exploited by Emperors in order to gain power.
An example of Imperialistic Political Power in Pompeii, you could mention the Riot that Tacitus records in AD 59 (check date!), as Emperor Nero intervened and imposed a 10 year ban on Gladiatorial Entertainment due to the Riot between the Pompeians and Nuccerians. Therefore, this demonstrates that even whilst still in Rome, the Emperor had complete control over the provinces throughout Italy.
And I'm too lazy to think of any more examples. Some of the examples overlap, so it's up to you how you would like to structure your response coinciding with the examples. I hope this helped somewhat. Good luck with your response. If you do need anymore help; I'll be able to give you some more help later (maybe once, I've had some coffee) Again, good luck. n_n