We can broadly divide the history of Indian commissioned officers in the British Army into two time periods, one prior to the Sepoy Mutiny (and thus concerned with the East India Company), and the second dealing with the British Indian Army, up to independence. Most of the information compiled here comes from "India’s War: The Making of Modern South Asia, 1939-1945" by Srinath Raghavan.

The East India Company Unfortunately, I can't really say much about early EIC forces, as I don't know very much about this time period, so we will limit ourselves to the state of the East India Company's Presidency Armies just prior to 1857.

Although the East India Company did raise some entirely European units, most of its forces were comprised of native Indians, with the army of the Bengal Presidency being comprised largely of upper caste Brahmin troops (the Madras and Bombay presidencies were, to my understanding, more diverse in makeup). Among the native infantry and native artillery units (artillery units of this sort would be disbanded following the Mutiny), commissioned British officers always outranked their Indian counterparts, regardless of seniority, and it was entirely possible for a fresh British officer to outrank a veteran native Indian. Further, promotion among the enlisted troops (European or Indian) was strictly based on seniority. The cavalry forces of the EIC were less hierarchal in this regard, and it was not uncommon for native Indian troops to gain high ranks in the mostly Indian dominated cavalry units, James Skinner, an Anglo-Indian of mixed parentage both raised and commanded his native horse regiments, and retired with the rank of colonel. Indeed, within cavalry and infantry units, quite a bit of responsibility was allotted to Native Indian officers, although they were formally subserviant to their British counterparts.

Most of this was completely upended by the Sepoy Mutiny, in the aftermath of which the Bengal Army in particular faced significant reorganization. Almost all of the old native infantry units were disbanded (many had mutinied and could no longer be fielded regardless) almost all of the native artillery units were disbanded, and the ratio of British to Indian troops was greatly increased. This being said, British officers worked much more closely with their Indian counterparts following the reorganization, but "close" is a relative term, and many British officers still considered themselves superior to their native troops. This would represent roughly the status quo of the British Indian Army up to the 20th century. There was some fluctuation in organization in the decades between, but I'm not very familiar with the specifics of organization in these years.

The British Indian Army in the 20th Century

During this period, Indian soldiers were not allowed to receive the "King's Comission," that is, they were not allowed to become commissioned officers proper in the army. Indians were limited to the "Viceroy's Comission," which, although it granted them the title and rank of commissioned officer, left them strictly in command of Indian troops only, and rendered them subserviant to all British commissioned officers. In 1917, however, the British government reserved 10 seats anually for Indians at the Royal Military Academy, largely in response to demands to "Indianize" the British Indian Army, as I understand it.

Indian political figures took a keen interest in these developments, but they protested that the rate of Indianization was far too slow. Muhammad Ali Jinnah, leader of the All India Muslim league was a particularly vocal critic, complaining it would take "centuries" to Indianize the army at the rate of 10 officers a year (there were over 2000 British officers alone in the Indian Army at this point). Concerned by scale of support for Indianization, British officials made a minor concession to the Indian Assembly, agreeing to Indianize eight segregated units with Indian commissioned officers.

Upon receiving this minor concession, the Indian Central Legislative Assembly proposed doubling the seats allotted to Indians at Sandhurst, and the creation of a large Indian military academy (proposed to be completed in 1933). Not surprisingly, the British government rejected this proposal, but it did increase the allotted seats at the Royal Military Academy to 25. A Royal Military Indian Academy was finally established in Dehradun (in modern Utterkhand) in 1932, however it accepted only 40 candidates annually, with a large portion allotted to the troops of princely states.

The outbreak of war significantly changed the landscape of the Indian Officer Corps, and the ratio of Indian Officers to British ones increased throughout the war. Officers during this time period were first screened by a local selection board, before progressing to a central selection board, and finally a very short stint at Dehradun. Despite this, the bulk of applicants were rejected either by their local selection board, or later, by the central board, and those that did make it through were argued to be of inferior quality (whether they actually were, I cannot say).

To quickly summarize, Indian officers did exist under Company Rule, but were officially subserviant to their British comrades. A similar pattern continued in the British Indian Army, however the number of white officers was greatly increased, and Indian officers remained in short supply well into the mid 19th century, with the quality and number of Indian commissioned officers generally being rather low (according to contemporary sources).