What is the prompt of a pikachu wagging a joycon mean?

I often get it after hard fights like gyms and bosses.

Its in the bottom left corner, and is simply a pikachu wagging a joycon from side to side.

I'm guessing it is a reminder that the 2 player mode exists? I'm using the red joycon and he has the blue one.

But I never got a tutorial or an in game explanation of what is that icon.

EDIT: Also, there's the constant reminder of the 2 player mode with the green icon, that is usually bottom right.

Solution 1:

That icon indicates that there's a special message relevant to your latest accomplishment if you play with your partner Pokemon. I'm not sure if this makes them like you more or not, but you can shake the controller when the icon is onscreen to automatically bring up the play screen.