It's fairly clear at this point that his cosmic radiation has killed everyone other than himself, Saitama, and Blast and co. (though possibly launching them off to Io had other effects on Blast, as we don't see him standing around). Child Emperor's hair fell out within moments, which is much faster than would happen with a minimal lethal radiation dose. There are a bunch of dead fish washing up on the shore, and water is normally an excellent shield against radiation. So we can pretty safely conclude that Tareo is, in fact, dead. Garou panics and mourns because he had envisioned Tareo as the first of the people he saves through his "absolute evil" plan. But instead he has killed him. So he has Saitama time-travel back before he had irradiated everyone to death to stop this.
You're right that he should have already been emitting at least some radiation. He was further away shortly before this, and as radiation power follows an inverse square law with distance that could be sufficient protection. Though given that people were having ruptured blood vessels in their nose before this just from the initial exchange with Saitama, it's not entirely clear that people haven't already had a lethal radiation dose, or at least a dose substantial enough to risk major health problems. Still, dramatically speaking, it seems the intent is that he arrives just early enough to save everyone from death. Presumably the tech of Child Emperor etc. would be enough to deal with the remaining damage, but only future chapters will resolve that. (EDIT: Indeed, Metal Knight has since shown up and strongly implied he could treat the radiation effects) It's pretty consistent with other Saitama feats—such as destroying the meteor—that he prevent deaths but not necessarily lesser damages.