They have to be exposed to a new strain of any other coronavirus in the wild, and that's when we'll see how their immune system will react when introduced to it. The "reaction" is basically an autoimmune disorder. The body begins hyperactively attacking to the point where it shows symptoms as rashes, blisters, swelling, etc. It's not so much the vaccine that immediately gives them that result, it's when the vaccine causes their own body's immune system to overreact and go haywire.