Cullen's wife never said that he was having an affair with his assistant... just that she knew he was having an affair.
Near the middle of the film, Kevin goes to Cullen to confront him about new information in the case: the day that Cullen's wife was murdered, she had met with a friend and said that she knew Alex was having an affair. The Cullens had signed a prenuptial agreement, which would be void in the event of marital infidelity.
Or, as Kevin puts it, "You fuck around, she gets rich."
Cullen admits to having an affair with his assistant, Melissa Black, and that he was engaging in this affair the night his wife was killed.
Later, however, when Kevin asks Melissa Black if she knows Cullen is circumcised, she doesn't know, meaning that she has never had sex with him and that Cullen is lying. So, if Cullen isn't sleeping with Melissa... who was he having the affair with?
Later in the film, at Eddie Barzoon's funeral, Cullen is with his stepdaughter, Alessandra, who despite being 14 is dressed very maturely in a black low-cut dress with heavy eye make-up and her hair down. After she takes off her jacket and sits down, Kevin sees Cullen fondling her skin with his fingers in an overtly sexual way, and he suddenly sees Cullen as Gettys, the child molester he had successfully defended in Gainesville.
It's made all too clear that Cullen was having an affair with his underaged stepdaughter. He murdered his wife not to protect his money, but so she wouldn't ruin his life by making it public that he had committed statutory rape.
It's debated as to whether Alessandra was an accomplice in these acts, but based on her appearance at the funeral and the fact that she had never reported Cullen to anyone, it can be assumed that she was a willing participant in both the affair and the murder.