Is there a specific term for when you get offended by a criticism which wasn't meant for you?
For example, person A says something not directed towards anyone in particular, but it was a criticism nonetheless, and it was intentionally meant to indirectly tell off some people.
Person B takes offense for whatever person A said, thinking that it was meant for him specifically; even when it was supposed to be for a group of people (which he may or may not be part of).
What has person B done, or what do you call the act of already claiming that you're guilty, even when the criticism wasn't for you alone?
I think I've come across an idiom for this sometime ago, but I can't remember what it was, nor where I found it.
In this situation I say to the offendee, "If the hat fits, wear it". Related when people think you're getting at them when in fact you aren't (slightly different from your scenario), the Biblical line, "The wicked flee when no man pursueth".
He is taking it personally.
to think that someone is offending you when they are not:
These criticisms should not be taken personally (= they are not meant to criticize any one person in particular).
[Cambridge]
So if you define a situation as "person B got hit by the rocks person A threw in no particular direction (but intended to hit people anyway)". In this case use friendly fire.
Also the related term is blue-on-blue.
Merriam-Webster's Eleventh Collegiate (2003) dictionary offers this as one of its definitions of umbrage:
a feeling of pique or resentment at some often fancied slight or insult
and this as one of its definitions of empathy:
the action of understanding, being aware of, being sensitive to, and vicariously experiencing the feelings, thoughts, and experience of another of either the past or the present without having the feelings, thoughts, and experience fully communicated in an objectively explicit manner.
So you might call the mental state in which a person feels offended by criticism not intended for him or her as "empathetic umbrage."