First, you've written in a comment that you do not remember whether you had instructions to report to the embassy, so it's hard to know the answer to your first question. In general, it's not necessary, but the fact that you are asking about it suggests that you may have been told to do it.
I don't know much about such requirements, and I haven't been able to find much about it on the internet. I do remember reading about such a requirement in some cases, probably because someone posted something here or on Expatriates Stack Exchange that mentioned it.
Second, you wrote
Considering the officer at the airport knew exactly when and where I left the country.
This is not correct. The US does not have officers inspecting departing passengers. Instead, for departing air passengers, they rely on submissions by airlines. If a traveler has a paper I-94 form, the airline is supposed to collect it and send it to the government. These days, the I-94 "form" is an electronic record.
Since it seems to have been some time ago, you may not remember whether the airline collected your I-94 form. If your departure was after the automation of I-94 forms, this is less of a concern, but to be safe you may want to assume that the US does not know when you left.
Under that assumption, you should probably
Gather whatever evidence you can to establish when you left the United States. A passport stamp from your return journey would be best. A boarding pass would be good to have, but if you do not have one then any other evidence of your presence in Vietnam will do.
Apply for the visa. Regardless of any effect your history may have on your application, the only way to find out for sure whether you will be granted a visa is to apply.
Bring the evidence in step one, along with the other evidence needed for the application, to your visa interview. If the officer asks you anything related to your return to Vietnam, especially if it has to do with reporting to the embassy, answer truthfully, and say that you have evidence to show when you returned.