Can you please upload screen shots of the layers and keyframes in the timeline so we can see what the problem
could be? It looks like one of the eyelids is reverse scaling. But I need to see your keyframes. Select the layers and hit the U key to reveal the keyframes.
I think the puppet pin you are moving of the eye that is upside down not in the right place. It should be on the edge you want to move and the other pins should be in the corner so you can pull the eyelid down.
A screenshot of the layer in Layer View with the Mesh revealed and the animated pin selected would help. I think it is just a case of improperly placed pins.
It would also help to see how your layers are set up. If you want to animate a blink with Puppet Pin you probably should create a layer that is the eyelash and eyelid closed. Then you add the pins and move the eye and eyelid up to animate the blink.
It is quite difficult to get a smooth arc using Puppet Pin to animate a blink. I would probably use scale, placing the anchor point somewhere near the upper part of the eyelid or use something like Mesh Warp or Liquify.
You can get a much better looking blink with a lot less work.
Another option is to simply animate a mask, create different shapes for the eyelid, or --- or --- there are a zillion ways to do this.
What Rick said . . . Plus . . .
Have you looked at Adobe Character Animator? It provides a much easier set of methods for animating characters and he a blink behaviour included. I'd really recommend that you take a look at it. There are lots of great tutorials to get you started;
BTW you can open Character Animator from inside the File menu in After Effects. In the Welcome screen you'll see links to example files.
Sorry for this issue. Did you ever find a solution? Please let us know if you have or if you still need help.