Here, in chapter 23, Atticus is referring to how "low-grade" white men "take advantage of a Negro's ignorance." He finds it absolutely despicable that "white men cheat black men," and he thinks that the white man who does "is trash." So, when he says that "it's all adding up," he means how all of these awful, despicable acts of racism and cruelty against black people are adding up. Pretty soon, black people are going to get sick of it, and they are going to act. People can only take so much, and Atticus feels that white people are going to have to answer for their horrible treatment of the black people. White people will have to atone, or pay, in some way or another, for what has happened in history.
The irony in this statement probably comes from the fact that Atticus says right afterwards, "I hpe it's not in you children's time," and, his children are threatened by that very same type of low-down white man that Atticus despises so much. Irony usually exists when the opposite of what is expected occurs; you would expect in this book that Tom Robinson's people, in retaliation for the injustices that eventually take Tom's life, would rise up and do something to make the white people, or person, responsible for Tom's conviction, pay. You would expect them to be fed up with it all and demand some sort of justice, or to harm Bob Ewell somehow. They certainly had the cause to be upset. But ironically, they don't. They accept what happens. It is Bob Ewell who reacts poorly, making and acting on threats, and putting Jem and Scout's lives in danger. Jem and Scout DID have to "pay the bill", in their lifetime, but it was not a black person demanding justice, it was from the very person that had been causing the problem all along. We expect the trouble to come from the black community, not from the person who had technically "won" and that is the irony in the statement.
I hope that helps a bit; good luck!