No Facetime icon for switching cameras

On my new iphone SE, 3rd Gen, when using Facetime, I can see the person I called, but they cannot see me. The video showing at my end is the rear camera, which is not showing on the called person's end. On top of that, there is no icon to switch between the front and back cameras, the only icon showing is an [ A ]. On my camera app, I can switch between cameras with a circular icon, except when I am actually doing video, where it is then replaced with a white button icon. Thanks,