I absolutely think that it should be made into one one day, too!
As you can see here, the Fengtian Clique controlled Northern Manchuria in 1918.
The first entry in the map legend means Fengtian Clique - they are shown to be in control of Manchuria in 1920 as well.
As for control, I'd say its an interesting matter, since the absence of a strong state on either side of the border during this time probably meant that slipping across the border was relatively easy, indeed, this was something practiced by nomads quite regularly. Also keep in mind that due to the extremly fractured state of China in this time, the Republic exercised de jure authority over all parts of China, but not de facto, instead having to cooperate and tolerate warlords in certain areas, some of them later 'legitimized', others not (Zhang Zuolin being one of the 'legitimized' ones, being the more or less official representative of Republican power in the area). This does not mean that these warlords led internationally recognized states however, as they were considered internal factions of the Republic of China, subsequently foreign affairs matters like the one you mentioned were handled officially by the Chinese government of the Beiyang government. It's another question entirely whether the respective regional warlord decided to act on these announcements. :P
Also, here are some quotes from "Japanese Intervention in the Russian Far East", as I did some research:
"Meanwhile American and Chinese ships were added to those of Japan and England in the harbor. Harbin and Manchuria in general were at that time the centers for the organization of counter-revolutionary forces, grouped about General Horvath, ruler of the Chinese Eastern Railway, and the Atamans Semenov and Kalmykov. Semenov was in control of the station of Manchuria (a city) while the detachments of Kalmykov were already active at the station of Pogranichnaya, carryin on thefts and shootings of peaceful people under the pretext of combating Bolshevism." (P. 5)
The declaration announcing the Allied intervention in Vladivostok was also signed by Col. Paris, then in charge of the Chinese cruiser Hau-Yun.
"The question as to active military intervention was settled, and the governments of the United States, Japan, Great Britain, France, Italy and China - the latter was also dragged in - solemnly addressed the Russian people [...]" (P. 5)
"After the first weeks of the joint occupation of Russian territory by Allied troops, differences between the Americans and the Japanese became quite apparent. The later quite openly declared their intention to hold the railroad in their own hands. [...]and to an agreement between the Allies of March 14, 1919, by virtue of which there was formed an Inter-Allied Railroad Commission, which took it upon itself to 'guard the railroad'. (The Chinese Eastern, the Usuri and the Siberian Railroads are meant.)" (P. 6)
"The Japanese assumed the guardianship over the Transbaikalia [...] and a portion of the Usuri Railroad, which work was carried out jointly with detachments of Russian counter-revolutionaries organized by them. The Americans guarded a portion of the Usuri Railroad [...]" (P. 7)
"On the basis of a military agreement with Japan, in August 1918, China, [...] and the Japanese obtained the legal right to establish themselves on the Chinese Eastern Railroad and to assume the guardianship of the road, and made use of their sojourn there (they held the Chinese Eastern Railway for about two years
) to consolidate themselves firmly throughout Northern Manchuria." (P. 7)
On the same page a Japanese encroachment upon further territory in Manchuria is mentioned and an official Japanese government release reprinted, which I can also quote if interest exists.
Mentioning of White Terror by Japan:
"Simultaneously, the Japanese organized the Chinese Khun-Khuzes (bandits) and directed their assault on the Russian population, and together with them engaged in a complete terrorization of the Russian Far East, both in a military and in an economic way." (P. 7)
Regarding the extend of Chinese help for the Allied cause:
"[...]Chinese Eastern Railway, which in accordance with an Inter-Allied agreement must be guarded by Chinese troops, and also by permitting their troops to interfere in railroad matters [...] In Imianpo, a station of the Chinese Eastern Railway, the Japanese shot and killed several Russian railway meN; similar attempts were made in Kahilar, where shots were exchanged between Chinese and Japanese troops." (P. 11)
Interesting to note here is that cooperation seems to not always have gone smoothly, with incidents like these happening as well.
There's also other very interesting information regarding the Soviet-created satellite Far Eastern Republic (which I think is not in the game yet?) and other tidbits of information here and there, which I will present upon further review if needed. All in all I'd say there is a strong case to consider the Fengtian Clique to be in an ambiguous situation between tolerating the White forces and actively collaborating with them at times - Zhang Zuolin was in any case definitely opposed to the Bolsheviks and Allied usage of the territories under his oversight can be verified.
I hope this has helped already!