I think it's pretty simple: god is dad. Kids run to parents when they are afraid. Fear drives people to seek an authority who has the ability to explain and provide support. It's the "sheep" syndrome humanity is afflicted with. Fear is the driver of all religions and catastrophic events cause people to fear. Where there is no fear, there is no god.

And people often don't. I am people and I didn't.

Sometimes people try to cover all the bases, including revisiting comforting childhood traditions, in hopes of gaining possible supernatural assistance. Of course it doesn't work, but they soon forget about it anyway.

I think it's a mistake to assume that most people's existential beliefs are very considered and thought through. When something happens to make people fearful or insecure, they tend to regress. That's not a major scientific discovery, it's a well known facet of human nature.

It's entirely unsurprising that a percentage of people who are normally non-practicing, who have not worked through their dread of mortality and other issues, might give in to nagging thoughts that they really should be more pious. I'd bet if you looked closely you'd find those people tend to have been raised in the faith they regress to, drifted away out of boredom but always felt slightly guilty about it, and then when god appears to smite them, they reconsider.

It's also entirely unsurprising that this is a temporary effect. Everyone returns to their normal emotional set-points and things return to "normal".

There's another factor at play here, I'll bet. Religion -- apart from its dogma -- does have something of actual value. That's community. When you're part of a community that's threatened, you want to be closer to the rest of the community, and it's not illogical to do that via church, particularly if it's the main mechanism for community and refuge that you are aware of or have access to. And even the more hectoring, authoritarian sorts of religious communities, sensing an opportunity, probably tone it down and soften up in hopes some of them will "stick".

Edit: I also wonder how many people express getting closer to others in the community by means other than church -- by pitching in with recovery efforts, volunteering with NGOs and government agencies and ad hoc neighborhood activities related to that. Not to mention simply making sure there's not a single person you love or care about that you haven't said "I love you" to. There are many ways to huddle around the campfire in a storm; studies examining how people relate to church may be just looking at a narrow aspect of it.

A saying often heard is, "There are no atheists in foxholes." That is just not true!

Never trust a study or even a follow up study. This is probably just anecdotal evidence. Religiosity probably has some volatility and varies with time.

Another saying atheists like is, "Correlation does not prove causation." The studies to which you refer show correlation but do not show causation. This leaves us to jump to the conclusion that god made the disaster. Of course thinking that is delusional.

Just a guess on my part, but I am thinking it might be because such natural events, as predicted in the bible, cause people to think it just might me the end times and they want to get on board before it is too late.