Sanity check needed: traffic circles

A quick search shows me that neighborhood traffic circle rules/etiquette are confusing in this city lol.

My understanding is that these smaller traffic circles are different from roundabouts in that you are supposed to yield to the right if more than one driver approaches at the same time. But surely we yield to anyone who is already in the circle before we get there, right???

I’ve always waited when another vehicle is in the traffic circle, but twice this week I’ve been well into the traffic circle when another vehicle approaches and barrels through. Tonight in Cap Hill some driver honked at me because I was already in the circle and did not initially yield to him. (He was driving too fast and wasn’t stopping, so I had to slam the brakes.)

Should I be yielding once I’ve started around and then another vehicle approaches from the right, or are these other drivers the jerks?

EDIT: Okay, I have agreement from folks that a person IN the circle has right-of-way. That said, people be cray, so everybody stay safe out there. (Are all the downvotes from the non-yielders?!) Thanks, everyone!