I don't know about the HBPuffer but here are some pictures of puffers that are puffed.
And here is one that would be more similar to your puffer than the previous Porcupine picture
I don't own any Puffers but I've read/heard that you shouldn't try to make them puff as it can be harmful to them. They puff when they are stressed or frightened. It is a defense mechanism---if something tries to eat them, they puff up so they are too big to fit into the prey's mouth.
I'm so jealous that you have a new puffer!
Claudia