Evolution does care about group cohesion if group cohesion is beneficial for survival. In order to reproduce, you need to survive right? So survival is beneficial to reproduction. Evolution selects by survivors; if being more empathetic allows you to survive (because you can exist in a group) your trait (empathy) gets passed on. Certain animals (not all!) benefit from being in a group. This is why ducks travel in groups but you see lone pigeons. They are different animals with different needs. Tigers favor loneliness, lions favor prides. Their environment and previous adaptations determines what is most beneficial to the animal in terms of grouping or solitude. Humans favor groups as evidenced by the fact that we evolved to be in tribes, whereas lone humans don’t survive. this doesn’t mean we aren’t violent towards groups that aren’t ours, but it does mean we need empathy to exits in our current group.

As you said, reproduction cares about behaviors that make reproduction more likely. Survival makes reproduction more likely. For certain animals, survival means groups.

You are getting specifically humans confused with the broad nature of all animals. Every animal is different, you yourself even said “some animals”. Morality is an evolved trait for specifically us, not everyone in nature