Tight closure/Geometrische Deformation/Charakteristik geq 3/Problem/en

Give, for every prime number ${}p\geq 3$, an example of an ${}{\mathbb {F} }_{p}[t]$-algebra ${}S$, an ideal ${}I\subseteq S$ and an element ${}f\in S$ such that ${}f\not \in I^{*}$ in ${}S_{{\mathbb {F} }_{p}(t)}$, but ${}f\in I^{*}$ in ${}S\otimes _{{\mathbb {F} }_{p}[t]}{\mathbb {F} }_{p}[t]/{\mathfrak {m}}$ for every maximal ideal ${}{\mathfrak {m}}$.

Is this possible for the ring ${}S={\mathbb {F} }_{p}[t][x,y,z]/(z^{4}-xy(x+y)(x+ty))$?