How did the generation who elected Rutherford B. Hayes and Benjamin Harrison feel about the electoral college?

Depends on the power of presidency

During the time of John Quincy Adams Federal government was mostly tasked with foreign relations and interstate commerce. Quincy was not even elected in electoral college, there was contingent election in House of Representatives. As we look at his presidency, we could see that he could not obtain Congressional support for some rather basic things (from today's perspective) like federal naval academy, national university, national observatory, uniform system of weights and measures across US etc ... Biggest accomplishment were some infrastructural projects like railroads and canals. This goes with the mandate of controlling interstate commerce. It should be noted that in his time there was no federal income tax, which was introduced only in Revenue Act of 1861. Federal government was funded mostly by import tariffs and excise taxes on certain goods like tobacco and sugar. Average US citizen would not travel that much, and was likely more concerned who is his town sheriff (or county and state officials) than who is US president. As said before, Federal government could influence price of his tobacco and sugar and not much more unless he joins U.S. Army or Navy.

Election of Hayes was much more controversial because it happened after Civil War when Federal government had much more power (both officially and unofficially) . It also could not be resolved in electoral college. In fact, opponent of Hayes, Samuel J. Tilden probably won elections as he has the support of Southern Democrats and tactically approved their segregation agenda and end of Reconstruction. Not to got into much details, but whole affair could be resolved only after Compromise of 1877. This compromise allowed Hayes to be a president, but effectively ended Federal meddling in Southern affairs. Federal troops were recalled to their bases, and full rights were restored to all Southern states, creating essentially status quo ante bellum minus of course institution of slavery which was permanently abolished. System of electoral college was not much debated, because Tilden probably won both popular vote and electoral college. Hayes himself did try to protect voting rights of Blacks in the South, but because of aforementioned compromise he could not do much, as Federal government essentially didn't have jurisdiction over that. However, he and his administration did some important work considering monetary policy which was increasingly Federal domain.

Finally, we have victory of Benjamin_Harrison over Grover Cleveland (an incumbent) in 1888. What must be said about that election is that popular vote advantage of Cleveland was small (around 0.8%) and probably would have been erased had Blacks were allowed to vote for Republican Harrison in the South. In any case, Harrison had solid advantage in electoral college, in fact many people voted for him in protest over some of Cleveland's policies, especially proposed drastic cuts in tariffs and Federal spending. Harrison got the support of protectionists and also those depending on Federal budget. Cleveland was being accused of being to much pro-British. In any case, it is now widely considered that Harrison fumbled his presidency which allowed Cleveland to be re-elected in 1892, only president so far to serve two nonconsecutive terms. I could not find any information about some broad discussion about electoral college in aftermath of 1888 elections, probably because difference in votes was small and suppression of Black votes. Most likely both sides were satisfied with status quo - Republicans because they could win in electoral college, Democrats because they could retain control over South. In case of switch to popular vote Republicans would probably demand better protection for Blacks by Federal government, something that already happened in Reconstruction Era. Democrats didn't want that so they kept electoral college.