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I'm having trouble understanding exactly what this person is saying to me. The
context being that I was asked a question by them, and after responding they
said this:

> そうでしたか！それを聞けて逆に安心しました…！笑

I believe: そうでしたか！ = Was that so!? And maybe: それを聞けて = Able to hear that and
...

But: 逆に安心しました = was oppositely relieved (?) Does this mean they became
relieved, and were worried before (the opposite of relieved), or something
else?
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question
meaning adverbs
Understanding what 逆に means in context with an emotion
It means "(I probably shouldn't have heard that) but when I could hear that, I
was rather relieved ."

逆に in this sentence means "on the contrary", "rather". For example,
失敗して逆に良かった(I failed, but on the contrary it was good).
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answer
It means the feeling of being relieved goes against what one might have
expected, perhaps contrary to what the person themselves expected.

> So that's how it was? Despite what [you/I] might've thought, I am relieved
> having been able to hear this explanation.

What exactly that expectation that was broken is depends on the context and
cannot be inferred with certainty here. One guess, which makes this sentence
less convoluted sounding:

> So that's how it was? I was afraid to ask, but hearing this explanation I'm
> glad I did.

Or perhaps:

> … Despite what you might think, I'm relieved you explained it to me.

(This would be the appropriate interpretation if your explanation might put
the person into an awkward position.)

It's also possible that it doesn't have any particular meaning at all and is
mostly a habit of the speaker.
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answer