Let $X$ be a smooth $n$-dimensional projective variety over $K$ of geometric origin from a $d$-dimensional family over a perfect field $k$. Assume that resolution of singularities holds over $k$ in dimension $d+n$. If $\theta$ is a closed $(1,1)$-form on $X$ with ample de Rham class $\{\theta\}$ and if $u\in C^{0}({X^{{\mathrm{an}}}})$, then ${P}_{\theta}(u)$ is a uniform limit of $\theta$-psh model functions and thus ${P}_{\theta}(u)$ is continuous on ${X^{{\mathrm{an}}}}$.