The question of evil, with regards to solitude and solidarity, has to do with the response people have toward the plague. With the town sealed off, some are separated from loved ones, but they are stuck with each other, a microcosm of any society: in any society, wherever you are, you are stuck with those around you. Do you isolate yourself or work together for the common good?
Father Paneloux uses the plague as a means to inspire hope, saying the plague is punishment sent by God. He notes that Othon's son's death is God's will (God works in mysterious ways) and cannot be questioned. It must be accepted. His actions could be construed as religious diatribes, but his intentions are to promote solidarity; not solitude. Cottard, on the other hand initially espouses solidarity, feeling connected to others maybe for the first time; later, he isolates himself, embracing solitude and uses the plague for his own profit.
Like Paneloux, Rieux, Rambert, Tarrou and Castel see the plague as something that simply must be accepted. But unlike Paneloux, they believe the plague is a random, unexplainable, and Absurdist event. It makes no sense, it is not a scourge sent from God, nor something that they brought on themselves. Camus' general Absurdist position (often referred to as Existentialist although the two terms are not interchangeable) is that seeking solidarity, and fighting the plague in spite of its incomprehensibility is the way to find meaning. I don't think the problem of evil is really a guiding theme, but choosing solitude or nihilism (giving up) - even if faced with hopelessness and futility - would be the choice closest to the evil option.
Whether it is fate, God's will, or the indifferent hand of a random universe, Rieux, Rambert, Tarrou and Castel fight, even if they believe they can't win, even if it is meaningless. The choice to fight and the communal fight itself are the meaningful actions.