In part 3 of "A Rose for Emily", the the townsfolk voice narrator explains that, a short time after the death of Emily's father, she had come into the acquaintance of a construction foreman from the northern states named Homer Barron. Homer was younger than Emily, brash, swarthy and uncouth, by the standards that Emily was raised under. More telling is the fact that he is clearly a drifter that goes from town to town. All of these details made it look extremely strange that, of all people, Emily would have let herself accept this sort of man as her companion.
The narrative also says that there were two instances when the people were feeling openly sorry for Emily: after the death of her father, and after the apparent desertion of Homer Barron right when everyone though she had finally found her first "beau".
The narrator says, that
a year after they had begun to say "Poor Emily" and while the two cousins were visiting her...
Emily boldly shows up at the chemist's and says the words "I would like some poison".
While the scene itself is passive enough, the aggression (or violence) that your question may be referring to is the way in which the atmosphere changes at the chemist's shop when he asks Emily, albeit nicely, the purpose of her buying the poison.
Emily, her haughty, genteel Southern ego ever present in every action, openly shows her dislike at being questioned by others. After stating that she just wants "the best they have", and that she did not care which kind, the druggist makes an allusion to the fact that his poisons can kill "anything up to an elephant".
Emily, always one step ahead, asks specifically for arsenic, and wants reassurance on its effectiveness. This is the part where things become awkward. The urgency in Emily's request almost illustrates her inner anger and resentment. We still do not know what has happened, or what she needs the poison for, but the rest of the scene speaks volumes of what would happen when that poison reaches the hands of Emily. Still, she had to answer the chemist's request
But the law requires you to tell what you are going to use it for.
Miss Emily just stared at him, her head tilted back in order to look him eye for eye, until he looked away and went and got the arsenic and wrapped it up.
This eye to eye showdown resembles a typical duel, or a shootout, between two rivals. In this case, we can clearly see who dominated who. This is what elicits the violent undertone of this specific moment.
The fact that this incident is even public knowledge (the townsfolk narrator is telling us all about it) shows that, at some point (before or after Emily's death), the poor chemist must have imagined that something bad would come out of this transaction, and told the people about it.
Back to the story, the chemist ends up obliging to Emily and sends the poison over to her home.
Juxtaposing two different scenes in one same paragraph, the narrative immediately switches to the moment that Emily opens the package, as it is delivered to her. Just as if she were answering the question the chemist had just asked on "what she is going to use it for", we see that Emily reads the package and, under the skull and bones that symbolize the deadly nature of the product, there are written words which read "FOR RATS".
A clear allusion to Homer Barron himself, the "violence" in this scene, once again, is passive-aggressive in that we know what the purchase of the poison entails: her emotions at the time, the potential acts of Homer, her want for revenge, her contempt for him, and the eventual consequence that will come as a result of the use of the substance.