I agree that Marten's flustered stammering makes it obvious that he's unprepared, but these people are operating under the reasonable assumption that Marten is a librarian, who has been entrusted the position by a senior ('You could use the extra responsibility', indicating that Tai thinks he's capable of handling it.)
Marten does nothing to halt that idea in its tracks, and continuing to spout inanities desperately then finally revealing that he's not actually qualified ('Aren't you more qualified' =/= I am unqualified) seems like a deliberate let-down. So yes, I can see how it can be construed of as a prank. And it doesn't have to personally malicious either, since this perceived 'hazing ritual' could be someone else's idea and put Marten up to it. In Ginger's eyes, it's not 'this librarian is the instigator of a hazing ritual and is deliberately mocking us', it's 'this person is complicit in a hazing ritual and we the interns are its victims'. The irresponsible mastermind could well be Tai, or anyone else. She doesn't seem to be personally offended by Marten.
I think it's perfectly reasonable to expect at least some modicum of competence and knowledge, even from an unprepared 'intern-trainer'. Surely Marten should have cleared the air before digging himself a hole. That is possibly the silliest training lesson I've ever seen.
About her posture: Yes, she's definitely invading his personal space in panel 4, and that's out of justified incredulity/anger/demand for answers. (WHY is someone who doesn't know what he's doing in charge of training us?)
Her posture in panel one is defensive, not aggressive. Crossed arms is a sign of being fed up and is a protective reaction. Only panel 4 is aggressive.
And yes, maybe she had a bad morning, or maybe just bad experiences overall. As others have said, it's possible that she's previously been the victim of bullying and reacts pre-emptively to potential threats. If this actually WERE a hazing ritual, and everyone involved acted exactly the way they do now (including flustered Marten), I think her reaction would be entirely appropriate. The only reason we're all up in arms is that we KNOW it's not hazing and Marten's not intentionally being condescending. Not everyone is capable of calmly absorbing all the available data, processing and analysing them, then producing the most carefully measured and diplomatic response.
So while her reaction isn't ideal, it's relatively light. No one's swearing, yelling, getting physical (other than in-your-face in panel 3 - anyone else remember when that witch poked Penny with her cane and everyone got heated up?). The situation is tense, but not explosive. The worst it's gotten is the not unreasonable leap-to-conclusion, and a 3-second invasion of personal space. I think that's getting off pretty light.
What Marten needs to do now is explain the situation, as he should have done at the beginning before the drama could begin (and before it worsens).
PS: Good god. Look at this wall of text!