If a paladin fails the saving throw against a Demilich's Howl and falls unconscious, are their allies frightened if they succeed on the save?

Question

The demilich (MM, p. 48) has the following action available to it:

Howl (Recharge 5-6). The demilich emits a bloodcurdling howl. Each creature within 30 feet of the demilich that can hear the howl must succeed on a DC 15 Constitution saving throw or drop to 0 hit points. On a successful save, the creature is frightened until the end of its next turn.

A party of adventurers faces a demilich. One of them is a paladin with the 10th-level feature Aura of Courage:

Starting at 10th level, you and friendly creatures within 10 feet of you can’t be frightened while you are conscious.

The demilich gets close to the party (who are all within 10 feet of each other), and uses its Howl action. The paladin fails the save, while their friends succeed. Are their friends frightened?

Relevant factors:

• The Paladin will be reduced to 0 HP, and thus unconscious. When that happens, their Aura of Courage will stop working.
• We know from Does a Paladin's Aura of Courage prevent or suspend frightened effects? that if the Aura of Courage is up when the frightened effect tries to apply itself, the Aura going down after that will not mean the effect resumes; it was initially prevented entirely, and so is not merely suspended.

So the only question that remains is:
Will the Paladin still be conscious at the point the Howl attempts to apply the frightened condition to the party? Or will they already be unconscious?

Answer 1

It is the DM's choice, since it's the demilich's turn

While it is only an optional rule, Xanathar's Guide to Everything offers us this on simultaneous effects on page 77:

If two or more things happen at the same time on a character or monster's turn, the person at the game table — whether player or DM — who controls that creature decides the order in which those things happen.

Thus in this case, as it is the demilich's turn, it will be up to the DM to decide the order in which the saving throws are made. I personally would choose "as the monster" and go for the option that is most detrimental to the PCs (i.e. paladin goes first), but others might be more softhearted.

Even without this optional rule, though, it's up to the DM how to resolve this, since there's no default/core rule that covers such simultaneous effects.