I'd argue that Sisko thought that he was solving the problem: if he stays away from the people he cares about, all of them, then they won't die.
It was frankly the coward's way out, IMO. Life is full of uncertainties--tomorrow isn't guaranteed to anyone. Sisko essentially walked out on his family out of fear and convinced himself it was the right and even noble thing to do.
From his perspective, mightn't this have been an easy thing to do?
He was under the impression, based on his year-long stay with the Prophets (who knows what his subjective experience of time was?), that if he stays in contact with the people he cares about they will all die, and that they already
have begun to start dying. Sisko's belief was sufficiently strong that he thought that things were at risk of deteriorating significantly if he stayed longer, and that staying to talk about it posed a mortal threat to their lives.
A question to you. What if Sisko was--is?--actually entirely right? What should he have done? What should he do?