  It is well-known that, for sufficiently mixing dynamical systems, the number
of visits to balls and cylinders of vanishing measure is approximately Poisson
compound distributed in the Kac scaling. Here we extend this kind of results
when the target set is an arbitrary set with vanishing measure in the case of
$\phi$-mixing systems. The error of approximation in total variation is derived
using Stein-Chen method. An important part of the paper is dedicated to
examples to illustrate the assumptions, as well as applications to temporal
synchronisation of $g$-measures
