Paimon appeared as a weird light flickering around places
I figured so that's how the movie could tell you who Paimon possessed at any one time, like Peter seeing the light, and then looking at his reflection to see it grinning back, stuff like that.
Also, when Toni Collette's character sees her husband spontaneously combusting due to trying to throw the book in the fire and that same weird light hits her, she suddenly turns from terrified to disinterested, to obviously show us the possession.
Heck, this film was fucking creepy!