How did William McKinley deal with the issue of imperialism?
It appears that President McKinley dealt with the repercussions of Spanish foreign policy, or the chaos created by the decay of the Spanish Empire. When Cubans revolted in 1895, Spain brutalized the population; The McKinley administration was nominally fighting Spain to free Cuba from repressive rule (see link.) However, once the war was concluded, it appears that other influences contributed to the US replacing Spain and being just as brutal, especially in the Philippines.
The US for the prior century had the concept of a "frontier" with which to expand American culture. By the late 1800's, the continent was more or less "settled," and expansionist tendencies moved beyond its ocean borders into the affairs of other nations. Had the US been truer to its own philosophies, perhaps it would have promoted the concept of self-rule to indigenous populations; the fact that it did or did not cannot be attributed solely to the president of that time; imperialism was not his alone to contend with, but perhaps he did look the other way. As Commander in Chief, he led the forces to free the repressed; what happened afterwards doesn't describe his active participation. However, the Spanish-American War, under McKinley's administration, sadly marks the beginning of the American Empire.
McKinley presided over a period when the United States took a great deal of what you might call its empire. During McKinley's time in office, the US annexed Hawaii and also fought the Spanish-American War. In this war, the US took control (either official or unofficial) over Cuba, Puerto Rico, Guam and the Philippines.
While McKinley was not necessarily the leading force behind this imperialism, he certainly did not try to stop it. So, in terms of imperialism, you could say that McKinley was one of the presidents who did most to give the US an empire.