What happens if a Sibriex targets the same creature with Warp Creature repeatedly?

The Sibriex monster, found in page 137 of Mordekainen’s Tome of Foes has an ability called "Warp Creature". For convenience, here’s the entire text of it: (emphasis mine)

The sibriex targets up to three creatures it can see within 120 feet of it. Each target must make a DC 20 Constitution saving throw. On a successful save, a creature becomes immune to this sibriex’s Warp Creature. On a failed save, the target is poisoned, which causes it to also gain 1 level of exhaustion. While poisoned in this way, the target must repeat the saving throw at the start of each of its turns. Three successful saves against the poison end it , and ending the poison removes any levels of exhaustion caused by it. Each failed save causes the target to suffer another level of exhaustion. Once the target reaches 6 levels of exhaustion, it dies and instantly transforms into a living abyssal wretch under the sibriex’s control. The transformation of the body can be undone only by a wish spell.

I’m aware that normally a creature can’t be "double-poisoned". If it is poisoned and gets hit with the condition again, the duration is simply reset. However, Exhaustion is a special condition in that it comes with 6 levels of severity.

I’m at loss as of how to interpret the wording of the Sibriex ability. If it has hit a creature with Warp Flesh, can it speed up the death process by using the ability again? Or can it only wait for six failed saves and hope the creature does not rid itself of the effect?

  • Does the sentence "Each failed save causes the target to suffer another level of exhaustion" apply only to end-of-turn saves or to saves caused directly by the sibriex using the ability again too?
  • If not, is there any benefit for it to try Warping the same creature twice?