As
store.happy-hg.com says, you get the items on the starting chest at your island. Therefore, you need to do /island reset if you want to spawn in a Mockingjay island with the Mockingjay items said above. Anyway, you will still get the "you don't lose hunger in your island" perk, even if you don't restart your island, as that perk doesn't depend of your mockingjay island.
Hope this info helped, if you have any other question please reply, and thanks for donating!