I would argue that an empire usually has possession of colonial territories. Often those territories have their own armed forces or militia that is made up of colonized peoples and commanded by officers or leaders from the metropole. One can find these elements in Portuguese, British, and Spanish imperial possessions. These were not limited to Europeans, however, as Nahua (Aztec) and Inca imperial forces often recruited from the frontiers to help bolster the size and scope of their military forces. See Hassig’s Aztec Warfare for his descriptions of Nahua recruitment and military expansion practices. The Spanish often used frontier peoples to help increase their armed forces in the 16th century. When Tristan de Luna came to Pensacola in the late 1550s, there were Nahua-speaking troops with him (Bense, Archaeology of Colonial Pensacola). Likewise, Restall (Maya Conquistador) has written that Maya troops regularly accompanied Spanish expeditions into other parts of Mesoamerica.

For the Inca, when new territories were conquered or pacified (the term the European conquistadors often used in the 16th century for their own conquests) local residents were forcibly removed and transplanted to new parts of the empire. By doing this, the local or ethnic culture was diluted and forced new imperial subjects to acclimate to the imperial religion and culture. As new peoples were forced into the Inca state, the armies and supporting forces increased in size. For example, peoples admitted to the state from the southern parts of the Andes might be forced to live in the area of Quito or the Amazon side of the Andes. By relocating these people, the Inca elite and ethnic lords were able to maintain power and prevent uprisings from occurring. When the Europeans arrived, newly relocated residents were some of the first to see that Inca power could be challenged successfully. Non-ethnic Inca peoples regularly saw European encroachment into Peru and elsewhere as a way to reestablish ethnic and cultural identities that the Inca had worked to destroy or suppress. Steve Stern’s Peru’s Indian Peoples focuses on this element in particular while Frank Salomon’s Native Lords of Quito demonstrates how northern communities operated to keep local elites and ethnic groups in power in the face of imperial domination (or lack thereof).

So, to sort of answer your question: imperial forces recruited the manpower they needed from the frontier or colonized peoples. By doing so, they limit the direct impact against the primary ethnic group and they force colonized peoples to assimilate into the imperial system.

The main reason is that it was easier.

This may not apply to earlier empires (but I can't see why not) but for the British in India, the recruitment of Sepoys (native Indians) was necessary to fight in India. Compared to most other European Nations, Britain at the time had a small standing Army - a professional army without conscription. This meant that there were limited amounts of troops available to deploy in India. The army was mostly made up of criminals, those tricked by recruiting sergeants or the very poor - people without a choice. This meant increasing numbers would be a difficult task.

However India had a far larger population, one that was conveniently in India - so wouldn't have to be transported there. There also was already a warrior culture in Indian society, for high caste Hindus being a 'warrior' was a source of pride (and with Muslims as well). You also had far more peasants willing to join - meaning it was far easier to recruit Sepoy troops than English troops.

But there is still the question of Loyalty. Before 1858 (the Sepoy Mutiny), in general the British were held in high regard by the Indians. The soldiers certainly had no quarrel with their officers (in general again, I'm sure there are specific examples contradicting this). By 1857, thing we're beginning to change. The East India company started recruiting the best of the officer corps to their civil arm - leaving Sepoys with incompetent officers. Also, an increase in missionary activity & annexation of Oudh drew tensions higher. This exploded in the Sepoy Mutiny of 1857. However, the Mutiny was crushed mainly by other Sepoys - the Madras and Bombay Armies stayed loyal, only the Bengal army rebelled. All that changed was a turn away from High Caste recruits to the 'martial races' of India, and a prohibition of Indians in the artillery.

This shows how the potential dangers of disloyalty were not as great from native populations as you may think - so long as they felt their culture was respected natives often cooperated with Imperial powers.

Tl:Dr It was far easier to recruit from abroad, often bigger armies could be raised (especially in regards to Britain) and the threat of disloyalty was not a prohibition to it - merely acted as a check to behaviour.