For one thing, Wiggins saw on that visit in March just how beloved players are at Kansas, where icons such as James Naismith and Phog Allen have become deified.
Wiggins also saw just how many players were departing.
Four senior starters delivered farewell addresses that night. A few weeks later, star freshman Ben McLemore announced he would be declaring for the NBA draft, leaving the nine-time defending Big 12 champions looking for a bunch of guys to plug into the lineup next season.
Undoubtedly, Wiggins saw in Kansas a place where he could shine.
"I just felt like that was the place for me," the consensus No. 1-ranked recruit said after announcing his college intentions Tuesday in Huntington, W.Va. "Going to college will get me better mentally and physically in the game of basketball."
Wiggins chose the Jayhawks over overtures from Kentucky, North Carolina and Florida State, where both of his parents attended and one of his teammates will be playing next season.
"I felt like there was a connection," Self said, "but basically, he picked a good night to visit. He visited on senior day and kind of saw what this was all about, a game that wasn't a huge high-intensity game, but a game he was able to see how players are beloved here."
Widely considered the next LeBron James - though Self compared him more closely to Tracy McGrady - the 6-foot-7 Wiggins initially was part of the 2014 class, but was immediately raised to the top of this year's recruiting market when he decided to reclassify.
Originally from Canada, Wiggins averaged more than 23 points and 11 rebounds while leading Huntington Prep School to a 30-3 record last season. He also dazzled scouts, most of which knew they had no chance of landing him, at the McDonald's All-American Game and Jordan Brand Classic.
The entire recruitment of Wiggins was unlike anything college basketball has seen.
Sure, he's the kind of transcendent talent that in bygone days could have jumped straight to the NBA, and that alone makes him unique. But by nature, he's a soft-spoken kid who cares little for the spotlight. So while other top recruits string along the public before making their college decision, Wiggins kept his thoughts largely to himself throughout the process.
Self said he texted Wiggins on Tuesday morning to wish him luck, and received a text back from the small forward saying, "Thank you." But besides that, Self had barely spoken with Wiggins in the final tense days of his recruitment.
Wiggins revealed his choice at a small ceremony at his prep school and with only a local reporter present. Self didn't even know he'd won the recruiting derby until he received a phone call from another reporter who'd heard the news.
"There wasn't jubilation like you'd think," Self said. "It was kind of a surreal feeling. I was so happy, but at the same time, it was almost a humble happiness, and so proud we were able to land Andrew to go with what's already a terrific recruiting class."
Along with losing McLemore, who's expected to be an NBA lottery pick, the Jayhawks are also losing star center Jeff Withey, forward Kevin Young and veteran guards Elijah Johnson and Travis Releford, who have never known anything but winning conference championships.
Kansas has a few reserves returning, including junior guard Naadir Tharpe and sophomore forward Perry Ellis, a five-star prospect that finally caught on late last season. But the Jayhawks will be dominated by newcomers as they chase their 10th straight Big 12 championship next year.
Wiggins is the headliner, but 6-5 Wayne Seldon from Tilton (N.H.) School is the second-rated shooting guard in the country. Seven-footer Joel Embiid from The Rock School in Gainesville, Fla., is the third-rated center. Guards Connor Frankamp from Wichita, Kan., and Brannen Greene from Tifton, Ga., are in the top 10 at their positions, and point guard Frank Mason from Massanutten Military Academy in Woodstock, Va., has steadily climbed into the nation's top 100 recruits.
"If anything," Self said, "it gets me excited to go to work."
Wiggins said the most difficult part of his decision was informing the three other finalists that he'd be going elsewhere. As for why he chose Kansas, well, he's keeping most of those reasons private, though he did say having his older brother Nick Wiggins at Wichita State was nice.
His father, former NBA player Mitchell Wiggins, said fit was also a big part of it.
"He liked their system. A lot of pro offense, the pick and roll," the elder Wiggins said. "The system is probably the biggest thing, and Coach Self is a pretty good coach."
Self is the first to admit he wouldn't be nearly as successful if it wasn't for his players - that's where it all starts, of course. But in luring Wiggins to Kansas, even Self acknowledged he's never coached another player like him.
"He doesn't really fit the mold of some of the guys we've had in the past," Self said. "He's a tremendous talent and a terrific kid. Probably an even better kid than he is a talent. We think he has a chance to be about as good a prospect as we've ever had."