We analyze a high-resolution N-body simulation of a live stellar disk perturbed by the recent passage of a massive dwarf galaxy that induces a wobble, in-plane rings and phase spirals in the disk. The implications of the phase-space structures and the estimate of the matter density through traditional Jeans modeling are investigated. The dwarf satellite excites rapid time-variations in the potential, leading to a significant bias of the local matter surface density determined through such a method. In particular, while the Jeans modelling gives reasonable estimates for the surface density in the most overdense regions of the disk, we show that it fails elsewhere. Our results show that the spiral-shape feature in the z − v z plane is visible preferentially in the under-dense regions and vanishes more quickly in the inner parts of the stellar disk or in high-density regions of the disk. While this prediction can be verified with Gaia DR3 our finding is highly relevant for future attempts in determining the dynamical surface density of the outer Milky Way disk as a function of radius. The outer disk of the Milky Way is indeed heavily perturbed, and Gaia DR2 data have clearly shown that such phase-space perturbations are even present locally. While our results show that traditional Jeans modelling should give reliable results in overdense regions of the disk, the important biases in underdense regions call for the development of non-equilibrium methods to estimate the dynamical matter density locally and in the outer disk.