In the Gaia era it is increasingly apparent that traditional static, parameterized models are insufficient to describe the mass distribution of our complex, dynamically evolving Milky Way (MW). Using realistic, cosmologically simulated galaxies from the FIRE suite, we test several methods for representing galactic potentials to determine which method best preserves the orbits, and orbital coherence, of tidal streams. We consider three classes of axisymmetric models to represent the potential of the galactic dark matter halo: a time-evolving low-order multipole expansion (TEMP), a time-fixed low-order multipole expansion (TFMP), and a time-fixed analytic model (TFAP). We calculate actions of tidal streams within three MW-like simulated galaxies at 300 time points from 6.5-13.8 Gyr for the three models, and utilize the action-space coherence of the stream stars, quantified by the Kullback-Leibler Divergence (KLD), to examine the fidelity of each model to the true galactic potential. We find that all three models, when appropriately fit to the mass distribution, produce clustered action spaces, with a decrease in clustering immediately after mergers with mass ratio (MR) of 10:1 or lower. However, for mergers with MR < 10:1 only the TEMP model successfully preserves action-space coherence at all; in the best case we lose approximately one stream’s worth of clustering. Furthermore, only the TEMP model has high orbital stability and low loss of information across cosmic time; traditional static models lose significant information and orbital stability as early as 0.5 Gyr ago, with total decoherence by 1 Gyr in the past. Our results underline the importance of a flexible, time-evolving model in describing the global potential of the MW.