Here are a couple of descriptions from academic sources. To put it very simply, it all boils down to a classic case of corruption and patronage. It's not necessarily the case that the system gave "citizens the impression of fair elections", but it gave enough people enough of what they wanted.
From Michael G. Burros (1982) "The Spanish Jury: 1888-1923":
During the Turno pacifico [sic], the Minister of Gobernación, whose functions were similar to the present U.S. Secretary of the Interior, held extensive negotiations with all power groups in the country. These discussions produced lists of candidates approved for election. Known as the encasillado, each list was sent to the provincial governors, all of whom were appointees of the Minister of Gobernación. The governors then took whatever steps were necessary to ensure that the local party leaders elected the encasillado candidate.
This structure depended upon the local boss, or cacique, for its existence. The cacique served to bridge the gap between his locality and the central government, as a party or government functionary, he maintained powers chiefly because citizen apathy resulted in low voter turnout. In order to deliver votes the cacique gave favors to his followers.The type of favor which the cacique delivered was often illegal; running the gamut from embezzlement to bribery. At other times the cacique asked government officials in the capital, Madrid, to suspend decisions harmful to his partisans. This system required the central government to ignore local corruption, which in most provinces took the form of patronage. In short, caciquismo was similar to the political machines which operated in the United States. (pp. 181-182)
Grau et al. (2010) "The political economy of infrastructure construction: The Spanish Parliamentary Roads (1880-1914)" provides more detail on all of the above. Just to quote one particularly relevant bit:
The specific promises and favours that might win local electoral support were
particularly diverse. The most frequent were perhaps individual benefits, including
exemption from military service, personal interventions in the judicial system, job
offers, etc. But, as discussed above, indivisible favours such as dams, roads, railways or civil buildings (schools, markets, etc.) were also very important. (p. 10)
If you read Spanish, it may be worth following through the footnotes in both of these sources for further detail.