This... may just be a weird artifact of the practice system, but I wanted to try out my shiny new d6's and, lacking any ability to Look For Trouble or otherwise beat up random guys in suits, I figured I would go to my favorite Aunt for a practice session (Free Fight, not the tutorial).
Only to be greeted by my old d4's. "Oh well, them's the breaks," I said, as I came to terms with the thought that the practice system wasn't set up for it. Being a bored dingus, however, I channeled my inner Daft Punk and went at it one more time. This time (and every subsequent time after), I had my newly-purchased d6's to play with.
Weird.
So I reloaded the previous save again and tried once more. Same result. The first time I use it I'm stuck with the d4's, after that I've got my d6's. This is repeatable, over and over. So then I changed things up. I had been going out to the garden to initiate the practice fight. Now I tried starting it from the war room. This time I had d6's right from the start. Again, this is repeatable.
If I initiate a practice battle from the Garden, the first time is with d4's. If I start from the war room, it's d6's. This is just for the first time practicing after upgrading your dice.
Odd, but not gamebreaking.