To clarify the Core Training aspect, what seems to be the case if you can get the training bags, and then set your Pokemon off 'against' them while you run around doing other stuff. Effectively, EV training by walking around.
My guess is that you'll see various kinds of bags for each stat, which increase at different rates and that they'll be consumable.
Though, between that and the actual mini game, the vitamins looks less and less useful. Yes, you can get a nice solid boost (to a set limit) in one go, but they're either very expensive or very rare. Super Training seems like an easier, quicker method all around.
Very glad to see them finally addressing this in-game with some solid features. They've skirted around the fact of EV training for a while now - pretty much as long as it's been a thing within the fandom. It's about time they actually embraced it in game. What they've done should also make it fairly simple for new players/people who've never understood EVs before to get into it. It'll make the crappiest of non-EV-trained in-game teams even more laughable, really.