The confrontation occurred when Quade removed Dempster from the game. Dempster, who had missed his previous start with hip and back soreness and a serious gastrointestinal disorder, had gone five innings and thrown 87 pitches.
An irate Dempster argued with Quade and threw several items in the dugout before exiting to the clubhouse.
"Everything is fantastic," Quade said Thursday, without revealing details of the conversation. "Do you want me to tell you the conversation I had with my girlfriend last night too? I'm sorry, but that's off limits as well."
Quade said things like this happen all the time in baseball.
"Look, that's part of being at this level, but not just in this town, but anywhere else as well," Quade said.
Quade and Dempster did not talk about the incident until Thursday afternoon.
"It's like anything else, if you argue with a player or a coach or just people in general at home," Quade said. "It was probably a different interpretation [by Dempster] of what was going on. Often times that's not considered during that moment, so it was good."
Dempster won his sixth game Saturday, one of two the Cubs won on a seven-game trip before wrapping up the first half of the season.
Bruce Levine covers baseball for ESPNChicago.com and ESPN 1000.