Well, it's not rational and it is very subjective - it's a reaction to what we're told about after all. There are horrible things going on all the time, one could live in a perpetual state of turmoil by bothering to find out about them.
What I wonder about is the relationship between emotional involvement and action. Generally I think it's people who are more detached, strategic and able to place things in context who actually do the work of tackling the issues that cause these tragedies. But, some emotional people do act and it's often an emotional response, or outrage at an injustice, that prompts examination of the wider issues and adoption of a course of action.
So, while I understand that some people are more outwardly emotional than I am, I do always want to ask what they're doing as a result of their feelings. I have little tolerance for example, for people who can only eat processed, packaged meat because the idea of eating a cutesy wootsey little lambikins, or confronting the reality of animal slaughter, upsets them. That is straightforward hypocrisy because there's an easy and obvious choice.
Getting upset by distant tragedy can be an expression of empathy that is hard to connect to the event but is played out in daily life though. So I'd perhaps distinguish between warm, empathetic people who are great friends and members of their own community and those for whom the upset is all about their self-image.