I'm not an expert on this period, but I can offer some answers. The evacuation of embassies had much to do with wether that country had been a combattant. The US? Yes, of couse they were evacuating. But remember that Australia, New Zealand, Thailand, and the Philippines all varying numbers of combat troops -- from a few hundred up to 12,000 in the case of Thailand -- fighting in Vietnam up through 1972. And largest of all, South Korea had about 50,000 soldiers in Vietnam. But countries like France, which were not belligerents, and had embassies in North Vietnam/DRV continued to operate. In the French case this was particularly important since several thousand French citizens still lived in South Vietnam, until the new regime began nationalizing their property and requesting they leave.

While most Americans made it out of Vietnam, some who were not in official government capacity stayed behind. One example is Sophie Quinn-Judge, now an historian who has written a good biography of Ho Chi Minh, but then was working for a religious NGO and opposed to the war. Nevertheless she and other Americans were arrested and held for several months, with most being release in the summer or fall of 1975 and sent out of Vietnam. Other Americans could seek refuge in foreign embassies. Some American journalists in Cambodia hid in the French embassy in Phnom Penh. I believe the only American who was not arrested, and was allowed to live in Vietnam during the 1980s when foreigners were barred, was Lady Borton, an American peace activist and writer whose works were extremely kind to the Hanoi regime, to the point of being propagandistic. Hence, why the communist government felt comfortable with her presence.

Foreign journalists like Hubert van Es, who took the iconic picture of an American helicopter evacuating Vietnamese from the roof of a Saigon office building, stayed behind (and were sure to wear flags of their home country on their sleeves, showing they weren't American). They were allowed to stay for several weeks before being escorted out of the country. I'd recommend reading Van Es' short recollection of those events.

But Van Es was a civilian and Dutch. Government officials from other countries did not make it out. Rhee Dai Yong was a South Korean diplomat working to evacuate Koreans, but never made it out himself. North Vietnam had a strong relationship with North Korea, and much was made in their propaganda of communist solidarity and 'American imperialism' being the same in Korea as Vietnam, as was the relationship between Ho Chi Minh and Kim Il Sung. Needless to say, being South Korean in communist Vietnam was not good. Yong was captured and spent five years in a concentration camp alongside the many Vietnamese also imprisoned. He wrote an interesting memoir of his experiences.

Hopefully others can contribute more detail.