Minecraft: 1.12.2
Forge: 14.23.5.2808

Mods: 6
Bookshelf-1.12.2-2.3.573
Cyclic-1.12.2-1.18.1
DarkUtils-1.12.2-1.8.0
Reliquary-1.12.2-1.3.4.786
ScalingHealth-1.12.2-1.3.33+135
SilentLib-1.12.2-3.0.13+167

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If your health is low but you have absorption and you take damage, it will proc the Phoenix Feather despite having enough overall health to survive a fatal attack. Example...

Note: Scaling Health changes the Health & Absorption rendering.

In the top part I have 3 Health and 10 Absorption. I touch some Diamond Spikes from Cyclic which deals 5.0 'player' damage. In the bottom part... the Phoenix Feather procs despite being able to survive the attack... however it took away 3 absorption after it revives me.

It also doesn't account for damage reductions from armor, protection enchantments, resistance nor modded damage reductions such as RPG Inventory's Buffed Gloves which cuts all damage taken by 20%. Angel of Vengeance which has a spell 'Shield of Faith' that cuts down all damage taken by 50%.

In this next example I am only wearing a full set of Diamond Armor using the Diamond Spikes from Cyclic which deals 5.0 damage, which is reduced to 1.25 damage if wearing a full set of Diamond Armor.

In the top part I have 5 health, wearing a full Diamond Set. I walk into the Diamond Spikes from Cyclic and in the bottom part it procs the feather even though the damage was reduced to 1.25 which is enough to survive the hit.

Damage was NOT scaled via Scaling Health during these tests.

One more thing to mention is that the Phoenix Feather ignores the 'Focus' Sash from Dark Utilities which if you have full health and take oh-so-much damage where it would be an instant kill... the Sash will leave you with 1 health remaining... but if you have the Phoenix Feather... that takes priority over the Sash meaning it revives you despite the Sash saving you from a One-hit KO.

On a side note, the Angelheart Vial also does the same thing as the Phoenix Feather where it gets used despite using the above methods... only it procs the vials per tick as long as you linger on the damage source, like a cactus or something.

If I used a Totem of undying instead... the Sash procs first and then the Totem if you took damage after it saved you.

Darkhax-Minecraft/Dark-Utilities#177

So... I've opened an issue with the Focus Sash on "Dark-Utilities" side and the Phoenix Down & Angelheart Vial uses 'livingAttackEvent' which is perhaps why the Focus Sash doesn't work as those items activates first before the Focus Sash. Focus Sash only works if you took fatal damage from full health.

Try changing those item events from 'livingAttackEvent' to 'livingDeathEvent'?