Yeah, it wasn't really reported on "accurately". You don't JUST play for 15 minutes, you have to also spam blocks for a bit.
I've finished unlocking everything this morning, but all my playtime last night didn't unlock a thing. The best thing to do is grab the white goal-box at the bottom of the screen(not the actual goal-button on-screen), drag it all the way to the right, then take a ground block(or anything really) and just fill in the gap two-high - tap and hold on the screen, hold left-control-stick to the right, and just lay down blocks all the way to the end, then head back the other way. 5 minutes later, you get the next-day-message. After that you can kinda swirl some twirls of blocks on each screen, stop, wait a few minutes, scroll to the next empty screen, swirl some blocks in real quick.... after 15 minutes of doing that at your leisure, you'll finally get a message saying the delivery truck "came early" and then you get the chance to play an example level.
Also, I'm not sure if it's true or not, but I think I had to actually USE the new items before it decided to give me the next set, but I'm not sure if that was a coincidence or not.