  Let $g \geq 2$. Let $M_{g,n}^{rt}$ be the moduli space of $n$-pointed genus
$g$ curves with rational tails. Let $C_g^n$ be the $n$-fold fibered power of
the universal curve over $M_g$. We prove that the tautological ring of
$M_{g,n}^{rt}$ has Poincar\'e duality if and only if the same holds for the
tautological ring of $C_g^n$. We also obtain a presentation of the tautological
ring of $M_{g,n}^{rt}$ as an algebra over the tautological ring of $C_g^n$.
This proves a conjecture of Tavakol. Our results are valid in the more general
setting of wonderful compactifications.
