I would have expected the Black soldiers to frag their White officers, "misplace" equipment, or openly go rogue. What kept these Black soldiers loyal enough to not do this and what convinced (other than desperate wishing) the Whites that they would be trustworthy?
Were they vetted followers of Abel Muzorewa who promoted loyalty to Rhodesia in exchange for better rights? Note that Abel would only come to power briefly in 1979 and the picture is from 1976.
Were they just paid extremely well?
The party line was that the war was not between Blacks and Whites, but between Rhodesians of all colours and international communism (Rhodesia Unafraid), that the communist-supported guerillas were a threat to Blacks as well (Anatomy of Terror), that they treated native Africans fairly (Rhodesia Accuses, 70s report) and that their opposition to a Black-majority government was an opposition to race-based politics (Ian Smith interview).
Beyond what the government wanted the world to believe, the lack of other economic opportunities led Blacks to join the army (Goodbye Rhodesia), and the government, stretched thin from over a decade of warfare, would make use of anyone willing to join.
British Empire armies the world over were natives. India is an important example. Indian troops were important in British colonial expansion to China during the Opium wars, and marched a long distance to fight the Ottoman Empire during world war I. There were even plans to have them march all the way to Germany, as they were highly skilled.
As people the world over are just about the same, there is no reason this would not apply in the African colonies. (It is well known that Africa was one of the first places to become civilized, in Egypt)
The British had a method of colonial expansion that followed a simple algorithm :
- Get a foot in the door, a local power base
- Extract wealth from locals.
- Send wealth to London. Induce local "balance of payments" deficit, ruining local economy.
- Economic issues spread to neighboring localities.
- With economic issues comes poverty. Hire strong impoverished teen age males to serve in the army. Feed them well, train them well, give them a feeling of power derived through service. In return, they will be loyal.
- Control new area, return to step 2
Of course, this applies to Africa as well.
 The best example of this is related to Tea, Opium, and the relationship between the British Empire and the Qing dynasty. According to , they learned how to do this within the Mogul Empire when expanding the British East India Company. It was also used in the African expansion. Because the Opium trade / wars are the easiest example, I will explain that.
Around 1750 - 1800 the British were importing a lot of Tea from Qing China. The only payment that the Qing would accept was silver. Britain was importing so much Tea around 1790 that the trade deficit was causing economic problems. They sent George Macartney to negotiate new trading rules so that the British Empire could trade goods instead of silver, reducing the deficit. For a variety of reasons, the Qing refused and maintained the silver requirement.
The British tried a bunch of ways to get this to change, and during the Napoleonic wars the figured out that they could grow Opium in India and smuggle it into China. It turned out (not surprising to us today) that Opium smuggling was very profitable, and that once you get customers, the are fairly "loyal".
This smuggling went on for a while, until Opium use combined with a loss of silver bullion was causing economic hardship and social breakdown. The Qing dynasty responded by shutting down the Opium trade, which sparked the Opium wars. The Qing lost the Opium wars, and the British got a bunch of small colonies in China and were free to trade as they pleased.
The areas administered by the British (Shanghai, Hong Kong, Xiamen) were originally small villages, and they quickly became the wealthiest areas of China. Why? Because the wealth of the Chinese hinterland was flowing out of China through these port cities.
Over time, the colonial possessions were gaining not just wealth, but also power. The power of the British and other Europeans and Japan was increasing throughout China, while formally the Qing dynasty was still in control.
The Qing Dynasty was a rich, powerful country. It was richer and had a better economy and a better educated elite in 1750 than any other part of the world. It took a long time for this society to crumble, and the elite understood what the British were doing, and some fought back.
In contrast, Africans were already quite divided when the British were moving in. Compared with the Germans and French, the British tended to leave the existing power structure in place and extracted just the wealth of the local area (Indirect Rule? Protectorate? Shaka Zulu). The British in the late 1800s had several advantages: They were really good at conquering and administering colonies, they were rich and industrial. They knew how to extract the wealth of the colonies.
Born in 1959, I saw as contemporaneous both Australia's involvement in the Vietnam War (1962-72) and the Rhodesian Civil War (1964-79). A brother was a member of the Australia-Rhodesia Society so we got monthly 'Updates' direct from Ian Smith's government. The same brother was liable to the 'draft' in 1972 but the new government abolished it. Gave our friends and family a keen interest in these two 'Cold War' hotspots. Why were blacks loyal to a 'White' regime? As Update told it, the ZANLA and ZIPRA forces were terrorists who used violence to enforce their rule.
As in Kenya, the Kitson method of 'counter-gangs' was used to deter them. Update estimated the rival guerrilla armies to have 30,000 men apiece with the government Army at 30,000. Was even a neutral force -Muzarewa's? - that allegedly had 30,000, too.
Why would blacks serve a white regime? Why do American blacks serve in the White-dominated US Army? Why did the South Vietnamese Army serve US interests,1954-75? It cost them 500,000 killed. Cannot be explained as 'they were well paid'. Is easy to forget the hysteria induced in us - and Them - during the 40 years-long Cold War. See the Rhodesian War in context: only then does it make sense.