Do creatures need to make a Saving Throw every turn they start in the range of the Aasimar's Necrotic Shroud, or only once?

Question

In the Mordenkainen Presents: Monsters of the Multiverse, the Aasimar's Celestial Revelation ability lasts for 1 minute, but does that apply to the Frightened part of the Necrotic Shroud?

Answer 1

The frightening effect of Necrotic Shroud happens once.

Celestial Revelation states:

you can use a bonus action to unleash the celestial energy within yourself, gaining the benefits of that revelation. Your transformation lasts for 1 minute or until you end it as a bonus action.

Two things are happening here:

• A transformation
• The effects of your selected revelation option

The transformation lasts for one minute or until you end it as a bonus action, and the particular revelation option you selected will tell you how it works. In this case, Necrotic Shroud reads:

Your eyes briefly become pools of darkness, and ghostly, flightless wings sprout from your back temporarily. Creatures other than your allies within 10 feet of you that can see you must succeed on a Charisma saving throw (DC 8 + your proficiency bonus + your Charisma modifier) or become frightened of you until the end of your next turn.

This is what happens when you activate your transformation. The effect that lasts until the end of your transformation tells you that it lasts until the end of your transformation:

Until the transformation ends, once on each of your turns, you can deal extra necrotic damage to one target when you deal damage to it with an attack or a spell. The extra damage equals your proficiency bonus.

The effect of the feature that occurs each turn is prefaced with "Until the transformation ends, once on each of your turns", which only comes after the feature has already described the frightening effect. So we conclude that the frightening effect happens once, when "your eyes briefly become pools of darkness, and ghostly, flightless wings sprout from your back temporarily", and the part that happens each turn is described after saying "once on each of your turns".