"It was completely exaggerated," White, 35, told People.com after Monday night's performances.
Show sources said White stepped on Johnson's foot during a rehearsal last week, then screamed at her because he thought she was overreacting about how much it hurt.
"Jaleel definitely was out of line," an insider told People.com. "It basically didn't have anything to do with Kym or her foot -- he was just stressed out and ready to snap."
People.com quoted the source as saying fellow "Dancing" contestant Donald Driver, wide-receiver for the Green Bay Packers, and pro dancer Mark Ballas "wound up having words with him. ... mostly trying to get him to realize that he needed to just get a grip already."
"This has been a stressful week for us, and people have stressful weeks. [Today] was horrible. I thought we got through it really well, and our dance tonight will show everyone that we really have a great connection," Johnson told the celebrity news Web site Monday.
When asked about the alleged incident, Ballas replied: "These things happen. This show is a competitive show. Things get heated. ... This got severely twisted. We've been in the same room all night, and everything's fine."
White starred on the 1990s sitcom "Family Matters" as a child and teen.