This took some trial-and-error for me, but I think i got it figured out:
When you create a new layer and set your base sprite, click on the layer name in the bottom right so the sprite is highlighted, and the emote selection will become a select/deselect toggle for which emote slots that sprite will appear in. In my setup, my neutral expression is in slot 1, so my base and blink sprite are in one layer and assigned only to that slot, and other expressions are set up the same way in slots 2, 3, 4, etc. Then all mouth shape sprites are on their own layer and apply to all emote slots