Aberrant Anatomy Clarification

I've a question about the Aberant Anatomy Dark feat.
It is about the warping flesh trait, it says  "Immediately after you make a D20 Test and roll a 1 on the d20"
So I'm wondering, what does it means for reroll abilities? Like, does warping flesh happens anyway, or I can use an ability, like heroic inspiration, to reroll and avoid the saving throw eventually?

Thank you in advance for the help!

Aberrant Anatomy

Dark Gift Feat (Prerequisite: Ravenloft Campaign)

Exposure to alien horrors like those of the Far Realm has warped your physical form in supernatural ways. You gain the following features.

Breathless. You can hold your breath for 1 hour.

Extrasensory Perception. You have proficiency in the Perception skill, if you lack it. You also gain Expertise in that skill.

In addition, you have Blindsight with a range of 15 feet.

Warping Flesh. Immediately after you make a D20 Test and roll a 1 on the d20, the aberrant influence infecting your form flares, wrenching control of your flesh. Make a Constitution saving throw (DC 13 plus your Proficiency Bonus). On a failed save, you have the Stunned condition until the end of your next turn.

Well, in the case of Heroic Inspiration, you can reroll “immediately”. 

HEROIC INSPIRATION

Sometimes the DM or a rule gives you Heroic Inspiration. If you have Heroic Inspiration, you can expend it to reroll any die immediately after rolling it, and you must use the new roll.

Since both Aberrant Anatomy and Heroic Inspiration are happening simultaneously, the rule about Simultaneous Effects applies: 

Simultaneous Effects

If two or more things happen at the same time on a turn, the person at the game table—player or DM—whose turn it is decides the order in which those things happen. For example, if two effects occur at the start of a player character’s turn, the player decides which of the effects happens first.

The Halfling’s Luck feature is a little less explicit about timing: 

Luck

When you roll a 1 on the d20 of a D20 Test, you can reroll the die, and you must use the new roll.

Personally, I’d also regard this as a Simultaneous Effect. 

I'm not sure if it's strictly RAW, but I've always considered reroll abilities to happen before any effects of the initial roll occur. A reroll replaces the original roll, so the effects of the new roll replace the effects of the original roll.