Once items are generated using drop tables or the give command, they become independant of the /item config. Therefore the only way to directly update items in the player's inventories is to use the Item Updater. You can either directly update the item you are holding using /updateitem, or enable the item updater for a specific item using /updateitem <type> <id>
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Updating physical items
Once the item updater is enabled for a specific item, every physical instance of that item is considered outdated and will be updated. An outdated item can only be updated once (performance save) when enabling the item updater, unless you apply further changes to the item. Every change you apply in the item edition GUI will make physical item instances outdated again till they are updated.
MMOItems updates every item in the players inventories whenever they log in. Furthermore any item clicked in a non-creative inventory undergoes an update check.