As wax eagle’s answer states, it appears that since “you cast” the spell using the item, you can use any of your character’s abilities that can be used “when you cast a spell”.
DMG P. 141 lays out the rules for items that allow the user to cast spells from them:
Some magic items allow the user to cast a spell from the item. The spell is cast at the lowest possible spell level, doesn’t expend any of the user’s spell slots, and requires no components unless the item’s description says otherwise.
and a little further down:
A magic items, such as certain staffs, may require you to use your own spellcasting ability when you cast a spell from the item.
In both quotes it says that the user casts the spell — not that the use of the item triggers the casting of the spell or any other wording. Thus abilities that you can use “when you cast a spell” are usable — you are very clearly casting a spell. No ability I have found says “when you cast a spell from your daily spell slots” or “when you us the Cast a Spell action” or anything else that seem to explicitly restrict it from applying when you cast a spell from an item.
Mike Mearls posted a not very certain reply stating “believe it’s only when you cast from your slots”
Jeremy Crawford has tweeted that casting a spell from an item is neither a Use an Item action nor a Cast a Spell action. The DMG section (p.141) that was supposed to clarify this mentions only the Use an Item action, and remains silent on Cast a Spell.
Nonetheless, it is not clear that whether or not something is a Cast a Spell action is what determines whether or not you can apply class abilities to the casting. What type of action something is is used to determine under what circumstances you may take that action. None of the class abilities say anything about “When you use the Cast a Spell action…” — the abilities simply say “when you cast…” while being agnostic as to what kind of action (or item?) is used for the casting.
How we have been playing it is that if you are using an item that uses the user’s spellcasting ability (such as most staffs), it is just as if they are casting from slots, except that a slot (and components) are not required. In that case you can use any special spellcasting abilities, such as sculpting, metamagic, powering your Arcane Ward, etc. When you are using such an item, the use of your own spellcasting ability suggests that you are interacting more directly with the weave, and doing more to actually create/shape the spell. The item in this case “merely” allows you to do it without using spell slots and components (and helps cast it even if you wouldn’t otherwise know how), but doesn’t provide a fully-formed spell for you. You have to bring the spell into being with your own spellcasting ability.
On the other hand, if you are casting from an item that does not use the user’s spellcasting ability (such as most wands), we are treating it as if the spell is essentially stored in the item “pre-formed” (with a fixed DC, shape, etc.) and can’t be modified, and thus (contrary to what is written) the user isn’t really casting the spell for the purpose of using/triggering special spellcasting abilities (but rather it was the creator of the item who had cast the spell, and the user is just commanding it to go off at a selected time). Thus, the user’s special spellcasting abilities cannot be used.