Here's what Yule and Burnell (Hobson-Jobson: a glossary of colloquial Anglo-Indian words and phrases) has to say under Competition-Wallah:
A hybrid of English and Hindustani, applied in modern Anglo-Indian colloquial to members of the Civil Service who have entered it by the competitive system first introduced in 1856. The phrase was probably the invention of one of the older or Haileybury members of the same service. These latter, whose nominations were due to interest, and who were bound together by the intimacies and esprit de corps of a common college, looked with some disfavour upon the children of Innovation. The name was readily taken up in India, but its familiarity in England is probably due in great part to the "Letters of a Competition-Wallah", written by one who had no real claim to the title, Sir G.O. Trevelyan, who was later on member for Hawick Burghs, Chief Secretary for Ireland, and author of the excellent Life of his uncle, Lord Macaulay.

The second portion of the word, wala, is properly a Hindi adjectival affix, corresponding in a general way to the Latin -arius. Its usual employment as affix to a substantive makes it frequently denote "agent, doer, keeper, man, inhabitant, master, lord, possessor, owner," as Shakespear vainly tries to define it, and as in Anglo-Indian usage is popularly assumed to be its meaning. (continues with quotations, the oldest being the [misuse] of Seton-Karr, 'Patriot-wallahs')

Partridge's Dictionary of Slang and Unconventional English:
wallah, in Anglo-Indian (hence in Army) compounds --e.g., competition wallah-- is simply a chap, a fellow: late C. 18-20. Only in certain (mostly, joc.) compounds (e.g., amen-wallah, base-wallah) is it eligible...
And British English A to Zed has it as
A servant or employee charged with the performance of a particular service. thus, the member of the household who worked the punka(h) was known as the punka(h)-walla(h), and so on... Applying the term to American situations, walla(h) would appear to come out simply as -man: the individual who repairs your typewriter is the typewriter-man; cf. iceman, barman, etc. A bag-wallah, in the old days, was a traveling salesman. Nowadays the term is either old fashioned or jocular, depending on its use.
And Sahibs, Nabobs and Boxwallahs: a Dictionary of the Words of Anglo-India has (as it probably should) the last word:
A suffixed morpheme expressing relation, denoting a person who does any act, performs any function, or is charged with any duty or belongs to any trade or profession, place, etc. Europeans commonly use it as a noun equivalent to 'man', 'agent', 'chap', 'fellow', etc. Used by Anglo-Indians in such hybrids of English-Hindustani or Hindustani-Hindustani as Competition wallah [1856], an East India Company official selected by examination; box wallah [1834], an itinerant pedlar [and, by extension, a European commercial traveller or businessman]; punkah-wallah [1864], a menial who kept the old cloth punkah going; lootie wallah [1782], a member of a gang of thieves; howdahwallah [1863], an elephant used for passengers; amen-wallah [19th-20th C.], an army chaplain, and by extension any reverend gentleman; base-wallah [1915], a soldier employed behind the lines, not in the front line; jungle-wallah [1826], a man of the jungle, uncivilized; Empire-Day wallahs, flag-wagging jingoists [Edmund Candler, Siri Ram Revolutionist, 1912]; oont-wallah-sahib, 'a camel-keeping gentleman' (Deccan Herald, 6 March 1984). poultice wallah [1870], a doctor's assistant, a para-medical; loose-wallah [1850], a rascal, thief; lemonade-wallah [1890], a teetotaler; janker-wallaah [1920], a soldier under punishment; jake-wallah [1900], a 'meths' addict; bilti-wallah sahib [1907], one who acts quickly; ground-wallah [1915], an R.A.F. non-flying man; goo-wallah [1900], a man of the sanitaary squad; gen wallah [1936], an information officer; jerrypurana-wallah [19th-20th C.] a dealer in old newspapers and bottles; Kabaddi-Wallah, Daddi-Wallah; barrow wallah, burra wallah [1914] the Big Man, the chief, No. 1; char-wallah [1933] one who supplies tea or a teetotaler; crab-wallah [1900], an evil person (fr. Hindi karab, 'bad'); admi-khane-wallah [1875], a man-eating tiger;. Agra-wallah [1776], a resident of Agra; banghy-wallah [1810], a Sweeper, Pariah, Untouchable; Sani-wallah [1875], a riding-camel-keeper. Pani-wallah = Beastie; Topi-wallah, Readymade Clothes Wallah [1894], an itinerant pedlar or ready-made clothes; Daddi-wallaah [Hindi. dari, cotton stuff, carpet], old clothes and junk man. Gao-wallah [1855], a cowherd; Ghar-wallah [1855], a maaster of the house; Putty-wallah [1850], an office messenger who wears a belt [Hindi patti]; And three related to special compounds, each one representing a particular form of Dharna (extortionate beggar): (1) Tasmiwallah, one who twists a strap around his neck and throws himself on the ground, a 'strap-rigger'. (2) Doriwallah, who thretens to hang himself, unless he gets satisfaction; (3) Dandi-wallah, who rattles sticks and stands cursing until he gets what he wants...