At work, someone yelled at me and spoke in a very rude way. The background was another supervisor told me to use a certain computer for a specific task, but this one thought it took too long and I should've used another computer. I didn't say anything when she yelled at me but at the end of my shift, I went to speak to her. I told her I knew the situation was stressful and calmly asked if she could try not to speak to me like that.
She got defensive saying I was being rude to her and that she wasn't mad at me. (we now have to wear masks in the workplace, which I agree make it more difficult to interpret a person's face and she pointed that out). I said OK.
Is there any way I could've handled it better? Any specific phrasing? Is it better to have these talks one on one or have other people around so they can't say I was harassing them? My manager likes to be kept in the loop about these things but I would prefer not to involve him if the problem is resolved. Should I let him know what happened or wait until it happens again?
To add clarity: I am not a supervisor. The person who yelled at me is. In general, we almost have as many supervisors as non-supervisors, and I've been getting a lot of conflicting advice. This is not the first time someone has spoken rudely to me at work, I have been trying to ignore it, but the other day another coworker approached me and told me he's surprised by the way other people talk to me. However, he doesn't want to go on the record saying it. Though it's not always yelling, several people speak in unprofessional ways such as making statements in overly demanding ways (e.g. "you! do this! now!"), lots of accusations or assuming I will do something wrong (e.g. "I've got my eye on you"), and just in general sounding and acting angry. The last sentence is not intended to be a rant. The point is that someone can act threatening in ways other than just yelling. In today's case, she said something weird about how I shouldn't listen to what people tell me so that I can avoid conflicting instructions... I think what she meant was she's only giving me advice on what she thinks the best way to do the task is. At the end of the day, she was yelling (whether she realizes it or not).