A virus cause genetic mutation in the parents.
A virus-induced mutation in the germ plasm of the parents. It does not alter their own bodies, but it does edit the DNA in the eggs or testes (thus in the sperm).
This mutation is dominant, and manifests in 100% of the offspring of post-plague parents.
It affects the function of the Pituitary gland in their offspring, making it release a malformed version of gonadotropins, which then proceed to wreak havoc on the poor kids. As the activation of these hormones is the exact thing that normally triggers the onset of puberty, it will strike with clockwork accuracy in its victims.
Sadly, because it it not a disease but an inherited trait, it will be incurable. Possibly symptomatically treatable, but incurable.
As asked in questions: Some scholarly comment and examples on viral alteration of reproductive DNA.
https://www.biorxiv.org/content/10.1101/2020.06.04.135657v1.full shows proof that human DNA has been "infiltrated" repeatedly, somewhere in our history.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6159993/ shows how the Zika virus causes Teratogenic effects by altering the DNA in semen.(actually in the seminiferous cells)
Usually viral teratogenic effects occur only directly, by the virus infecting the embryo as the mother gets the virus during early pregnancy. Even more often the mutating effect is only due to a chemical/hormonal imbalance effect during embryo development. Effectively the toxins from being ill "poisoning" the child within the sick mother.
But sometimes, the virus can infect and alter cells without killing them. And if these cells happen to be the sperm-producing organs of the male, or the eggs in the female, the results can be a permanent editing of all subsequent offspring.