k, so only Observer A makes a light pulse. Both images are of Observer A.
Image one is what Observer B sees when looking at A. This is because A is moving, B sees A in the position shown in the first image. I hear ya ghwellsjr about the pictures not being very clear. In the first image, observer B is seen near the top of the circle, at the end of the blue line that indicates the motion of A.
Image two, is how Observer A would see them self.
In the second image A observes them self in the centre of the circle.
For you to spot the "fallacy" in the scenario, you have to understand which frame each image is observed from. Is it clear now?