Originally Posted by Raiden
You actually get the reward in your inventory, but you have to look to see what it is. It could be CP, an armory item, or the conveted weapon Hot Shot. I got the Ruby Quartz item for armory, after I did a bit of a search after I finished the 5 battles. You should refresh the game to make sure, as well.
They should at least release patch notes to tell people that. I don't have a horse in this race yet because PVP is a waste of time and I really only do it if it's needed in SO and to get my typical 100K silver. Other than that, I have no illusion of getting any higher level or willingness to try that hard.