The Toy Day event is pretty lame actually... Jingle gives you a "Magic bag" that you give each villager one present out of. There are no "unique" gifts. You just give every single villager a "present" but it isn't actually an item. It's just part of the event. So there is nothing that can show up as far as I know. They don't open anything. That being said, after the event is done, you can give your villagers anything wrapped in the festive wrapping DIY you get at the start of the event and they'll give you one random "toy" item back from the new update.