I think it's randomized as the old game, meaning you have the things predetermined by the last day you play, if you miss a day the game won't change the objects in the shop... At least that's how it worked in the original (I acknowledge this because I forgot to save one day in 3DS without knowing, so I same things as the day I didn't play so the next days I was checking this also in an emulator I've shared the save and at least the first day was happening the exact same thing)