The first person arms in the demo are only visible if you have an item equipped. The third person arms are always animated as they are part of the humanoid rig, and you use them for the shadows.
The visibility is controlled via states with the ThirdPersonObject component that is assigned to your third person arms. If they are visible, you can check on that component, which state is active. So, you can decide whether you want to use first or third person arms in first person view.
For the first person arms you need separate animations. Are your first person arms animated when clicking the button?