No, they have to yield to YOU because you're already in the roundabout. It's hard to believe, but trust me, this is just how it works and all of the links I've posted agree. The reason why it works is because when you're in the situation you describe, for the person entering at the second exit to be a factor, they would have to be entering as you're already alongside the second exit and in the process of exiting at the third. So they need to be yielding to you as they will be crossing your lane. Part of waiting for the gap is waiting for the exiting traffic to clear. Not for only YOUR lane to be empty.