The British acted quickly in 1890 by basically doing the most British thing ever and just declaring that Zanzibar was now officially a British protectorate.
The British then installed their loyal puppet as the sultan and Zanzibar remained a British protectorate for the next 67 years without another violent uprising again.
The French protectorates of Morocco and Tunisia were ruled by Arab monarchs, and the French also ruled through native kings in Laos, Cambodia, and Vietnam.
Even further, what became Kuwait had also been a formal part of the Basra Province under the Ottoman administration until the British showed up and transformed it into a protectorate of theirs.
A rebellion in the British protectorate of Basutoland, known as the Gun War, had broken out over Sprigg's enforced disarmament policies – and it led to his resignation in 1881.