So I just finished the Taimi’s pet portion of the EP 5, and a notification appeared saying that, among other items, I got 2 of an item that shoudl grant me EXP. But the item was not on my inventory. 
Did not get reward fro Taimi's Pet
I think most of the EXP items from LS3 are auto-consumed upon receiving them. Their description/tooltip should state this.