The Treaty of Portsmouth only saw the South Manchuria Railway transferred to Japanese control, while the rest of the China Eastern Railway system remained in Russian hands. The South Manchuria Railway (Mantetsu), ran from Dalian northwards to Mukden then on to Changchun, while the Russians retained control of the northern portions of the rail network from Mukden to Harbin, as well as the east-west Transmanchurian Railway, and would continue to do so until 1935. Importantly, while the Russians had a great deal of influence and interest in Manchuria, they did not directly control the territory, which remained under Qing administration. Rather, the Russians held a lease on Port Arthur in Dalian, while also holding concessions for the construction of the railway granting them significant executive authority over the railway itself, and a thin strip of land on either side. While I can't speak to the precise details of what city governance was like during this period, Harbin remained a key node for operation of the China Eastern Railway, as the connection point between the north-south and east-west trunk lines. With the outbreak of the February and later Bolshevik Revolutions in Russia and the ensuing Russian Civil War, the Russian portions of the China Eastern Railway would be operated by elements of the White Army operating in the Russian Far East.

At the same time as all of this, of course, China was undergoing its own series of crises. The Qing Empire would fall in 1912 following the Xinhai Revolution and the Republic of China proclaimed in its place. The Republic would succeed the Qing in its official administration of Manchuria as a whole, while the Japanese and Russians would maintain their leases on Port Arthur and their respective portions of the railway. For Japan in particular, this railway was of vital importance in expanding its interests in Manchuria, both as a means to rapidly deploy troops into northern Manchuria in the event of a renewed war with Russia and a source of profit and further economic expansion. However, with the death of Yuan Shikai in 1915 and the rise of the Warlord Era, Manchuria became to home base for Zhang Zuolin's Fengtian Clique. Zhang was heavily supported by Japan in terms of both finances and weapons, and his forces saw some significant successes, even taking Beijing and much of northern China for a time. While still nominally a part of the Republic of China, Zhang's territory would be effectively independent under the Fengtian Clique, and would remain so till December 1928, where Zhang Zuolin's son, Zhang Xueliang. Following the assassination of the elder Zhang by the Japanese in June 1928, the younger Zhang would proclaim his allegiance to the new Nationalist government being formed under Chiang Kai-shek and raised the Nationalist flag across his territory, thus--technically--seeing the re-establishment of Republican authority across all of Manchuria. During this period, there were some disputes over management of the Russian portions of the Chinese Eastern Railway, as management was jointly shared by both the Soviets and Chinese governments, however, control would ultimately solidify under the Soviets, who took over the previously Imperial Russian concessions.

Of course, three years later, the Japanese Kwantung Army would stage the Mukden Incident as an excuse to invade Manchuria, driving out Zhang and his forces (who would go on to play a major role in the Xi'an Incident in 1936). From this point, the Japanese via their Manchukuoan puppets would exercise control over the territory, recognising Manchukuo as an independent government, and seeking to bring other nations in line with recognition of Manchurian independence. There were some question of whether the Soviets would intervene as Japanese troops moved into northern Manchuria, but there was no actual intervention from Soviet military forces. As the Japanese moved to solidify their control of Manchuria via Manchukuo, the Soviets would eventually opt to sell their interest in the Chinese Eastern Railway to Manchukuo, where it was folded into the Manchukuo National Railway, ending Russia control of the railway...at least until 1945 where the Soviet invasion of Manchukuo saw the formerly Chinese Eastern Railway transferred back to Soviet control until its final return to the People's Republic of China in 1952.

To summarise, Harbin was never directly under Russian control, though as a major nexus point for Russian railway interests in Manchuria, it hosted significant Russian influence. The end of the Russo-Japanese War saw only portions of the rail network south of Harbin transferred to Japanese control, and the remaining portions would remain under Russian (in various guises, be they Imperial, White, or Soviet) administration until the sale of the railway in 1936. Harbin itself would remain under Chinese administration, again in various guises, raining from Qing, to Republican, to warlord clique, to Japanese puppet government (though I suppose the latter would be better described as Manchu administration). I apologise for being unable to delve more deeply into the details of city governance in Harbin in this period, but hopefully this helps to answer your question.