The problem is that when Auto Blink is triggering your blink layers, it also hides all other layers in the same layer group. Since your eyebrows are in the same group, they are hidden while the blinks are happening.
To fix it, use a folder arrangement in PS where the blink layers are in a group with the other layers that should be hidden when the blink (or wink) is triggered.
For example, this is how the built-in Chad puppet does it: