Funnily enough, for Seoul, a US Air Force team was sent into the city after its first liberation (and subsequently had to flee before the Chinese offensive reached the capital), and two of them authored a book: Riley Jr., J.W. and Schramm, W., The Reds Take a City: The Communist Occupation of Seoul (Brunswick NJ, 1951). The authors took a number of first-hand accounts published following Seoul's first liberation and sought to put these in context with their own observations.

Riley and Schramm note how the North Korean government had put considerable effort into planning for the occupation of the South, swiftly placing their agents in control of the organs of local government. Whilst local communist cells may have taken over in some places, they were eventually replaced by officials imported from North Korea itself as the regime sought to impose strict control. This was likely an extension of Kim Il-Sung's distrust of the South's communists, and he notably did not get on well with their exiled leader, Pak Hon-Yong (who was purged in 1955).

But what did the occupation actually mean in practice? Early on, a number of typical wartime measures were implemented - identity cards became mandatory, whilst curfews and blackouts were imposed. The Bureau of Internal Affairs took over policing, seeking out 'reactionaries' involved with the ROK government, whilst those allowed to retain their roles of high social standing (teachers, doctors etc.) due to socialist affiliations became subject to political education and indoctrination through group meetings, lectures and sessions of 'public denunciation'. Such education was already the norm in North Korea, so this aspect of the occupation reflected the communist intent rather well.

Furthermore, some of those with ties to the regime could expect an increase in their quality of life. Political prisoners were released as the various prisons across Seoul were broken open upon the KPA's arrival on the 28th of June 1950. Some of these prisoners were immediately placed as judges in impromptu 'people's courts' or reappointed to their former positions as teachers and the like. You can see the attitude in one account of the occupation, where a boy's father had left home a few weeks prior. Shortly after the city came under communist control, the father then reappeared in a KPA uniform and gleefully told his family “You have nothing more whatsoever to fear…Remember, you are the family of a lieutenant of the People’s Army.” Bear in mind, these affiliations could also be used by clever individuals against the regime. Though not specifically in Seoul, one account tells of a woman who was able to avoid communist agents searching her home (wherein her partner was hiding) by threatening to withdraw her application for membership of the Committee of Women's Unions in protest.

Not all were so lucky. Terror became the order of the day as political 'reactionaries' struggled to hide from the communist authorities. The regime would seek out individuals, whilst those seeking to ingratiate themselves with the occupiers began informing on their friends and neighbours. Some targets were South Korean soldiers who were left stranded when the Han River bridges were blown prematurely during the evacuation, and could expect to be shot upon capture. Many others were subject to more of a psychological terror, being routinely arrested and subject to interrogation or 're-education' before being released for a time. Often those captured were also forcibly impressed into the KPA in some capacity, usually as forced labour but also as soldiers, and some of the accounts I've read note that as the occupation went on and the North Korean offensive lost its momentum, the conscriptions increased to supply the now exhausted army.

For those left in Seoul, the main struggle revolved around food. Over the course of the occupation families sold the entirety of their possessions in order to scrape together just enough to get by and avoid starvation. Those who had been lucky enough to stock up in the few days after the war began promptly lost their stores, requisitioned by the communists as 'donations'. Reading the accounts, hunger and starvation feature almost universally. By contrast, the Bureau of Internal Affairs were able to provide their officers (and even those they arrested) with meals of beef soup and white rice.

So as you can see, the occupying regime had been planned before the invasion of the 25th of June and effectively stamped its authority on Seoul. It kept the public under control by tightly controlling the supply of food, whilst also applying a systematic terror programme. Those affiliated with left-wing groups benefited from the regime, rising to a new status in society. Those linked with the South's regime, however, suffered, with soldiers and police officers being shot, and officials being key targets of the terror. The greatest suffering, though, was inflicted upon the general population of Seoul, who struggled to survive from day to day until US forces marched through the city once again. It's quite telling, in fact, that another recurring event in accounts comes with the Chinese offensive. Many who had stayed in Seoul in June were now resolved to join the exodus, desperate not to return to that miserable state of affairs which had already once been inflicted upon them.

Unfortunately I can't comment on the UN occupation of Pyongyang, but hopefully someone else can!

For sources, I would recommend the above The Reds Take a City, along with the following (all in English, I'm afraid my Korean isn't very good yet!):
For an insight into the North Korean regime within North Korea: No Kum-Sok, A MiG-15 to Freedom (Jefferson NC, 1996).
For military accounts of the initial flight from Seoul: Paik Sun-Yup, From Pusan to Panmunjom (Washington DC, 2007) and Lee Chi-Op, Call me "Speedy Lee" (Seoul, 2001).
For accounts of (or which include) the occupation: Millett, A.R., Their War for Korea (Washington DC, 2002); Chang, H. (ed.), 6 Insides from the Korean War (Seoul, 1958); Yoo Young-Bok, Tears of Blood, trans. Paul T. Kim (Bucheon, 2012); Hurh Won-Moo, "I Will Shoot Them from My Loving Heart" (Jefferson NC, 2012).

As someone already accounted for the occupation of Seoul, I'll try to talk about the UN occupation of North Korea.

Following the Korean War, the US and all other countries were depicted as 'crusaders' (십자군인) by the government under President Syngman Rhee whose position had been saved thanks to the UN intervention. In reality however, the War had taken a huge toll on the country; civil administration had almost completely collapsed, meaning that it was up to the UN and the South Korean army to administer territory still held in the South. In practice though, UN activities were limited to refugee control and interrogation, and keeping open the most important roads/railways (read: the ones leading towards the frontline). This meant that the transportation of goods for civilians was largely neglected. Similarly, other government services like schools, hospitals etc were all put behind the war effort which in practice resulted in them being largely or fully neglected.

The occupation of North Korea saw a similar problem in which civil affairs were often ignored in favor of military ones, especially since the official body ruling over Northern occupied territory was a military one: since the official goal of the UN operation was to restore the status quo that had ruled before the start of the war, South Korea's authority over occupied North Korean territory was not recognized by the US army and its allies. Similarly to what it had done in European and Asian theaters during and after WW2, the US military had planned on establishing a military government in all areas above the 38th parallel. As a result, all civil affairs would be in the hands of UN forces. Because of the humanitarian image the UN wanted to show this occupation was dubbed to be 'civil assistance' (민간원조 - Minganweonjo).

The organization that would carry on day-to-day affairs in occupied areas was UNCACK (United Nations Civil Assistance Corps Korea). This organization almost immediately fell into conflict with the South Korean government, which thought itself the legitimate authority in all of Korea and aimed to arrest communist sympathizers and interrogate the local population to root out supporters of the Northern regime. As a result of UN attempts to prevent such persecutions, small-scale conflicts would break out between Korean and UN authorities which would occasionally escalate into brawls between Korean and UN soldiers. The lack of a unified effort and the inefficient use of the UN's resources due to collisions with the Southern government did much to hurt UNCACK's reputation among local North Koreans. From their perspective it seemed as if rules could change anytime; some days people would be arrested, interrogated, beaten or simply shot at, while on other days they would be fed and given medical care. The image of arguing South Koreans and foreigners probably also didn't do anything to improve North Koreans' opinion about the UN's professionalism.

To conclude, similarly to the Southern areas of Korea, military affairs took priority over civil affairs and humanitarian activities in the North. Because of this and because of the Southern government's insistence on ruling over all of Korea, UNCACK never really managed to set up an efficient system to handle civil affairs in the North before the UN was once again pushed out by Chinese/North Korean forces.

Source: 김학재. (2009). 전쟁과 일상: 주한유엔민간원조사령부(UNCACK) 자료를 중심으로 ; 한국전쟁과 "인도주의적 구원"의 신화 -북한점령시기 주한유엔민간원조사령부(UNCACK)의 창설과정과 성격. 사림(성대사림), 33, 1.