This work explores autoencoder-based neural ordinary differential equation (neural ODE) surrogate models for advection-dominated dynamical systems. Alongside predictive demonstrations, physical insight into the sources of model acceleration (i.e., how the neural ODE achieves its acceleration) is the scope of the current study. Such investigations are performed by quantifying the effect of neural ODE components on latent system time-scales using eigenvalue analysis of dynamical system Jacobians. This work uncovers the key role played by the training trajectory length on the latent system time-scales: larger trajectory lengths correlate with an increase in limiting neural ODE time-scales, and optimal neural ODEs are found to recover the largest time-scales of the full-order (ground-truth) system. Demonstrations are performed using datasets sourced from numerical solutions of the Kuramoto-Sivashinsky equation.