Magic items like the Staff of the Magi let you cast certain spells from it as an action, including Conjure Elemental which normally has a minute long casting time.
The Staff of the Magi is not the only exception; a more extreme example is the Staff of Woodlands which can cast Awaken this way, which is normally an eight hour long spell.
Is there any resolution to how these different rules interact?
Best Answer
Yes, magic items can and do allow you to cast spells with long casting times as actions
Here, you are giving examples of items that are giving specific rule that contradicts the general rule on casting times.
The DMG even states that some magic items can modify the casting times:
The Staff of the Woodlands is indeed one of those exceptional items. It says:
The rule for this staff says that you use an action to cast a spell. The fact that one of those spells is awaken (normal casting time 8 hours) does not matter. That casting time is now superseded by the effect of the magic item.
Thus, any similar magic item that has some effect in it that modifies the casting time, will similarly override the general rule. In this way, magic items can indeed allow you to cast spells using a shorter casting time than normal.
Other effects can modify casting times as well
Spells (eg Wish), metamagic, and other features already exist to modify the casting times of spells. So magic item use is far from the only example of a specific effect overriding spells' casting times.
Jeremy Crawford also explicitly agrees with this:
And he also agrees in the very similar case of the necklace of prayer beads: