Dynamic mode decomposition (DMD) and its algorithmic variants have become commonly used techniques in the analysis, prediction, modeling, and understanding of nonlinear dynamical systems. In particular, these techniques are of interest for liquid injection systems due to the inherent complexity of multiphase interactions, and extracting the underlying flow processes is desired. These methods extract spatio-temporally coherent modes, which serve as fundamental processes that govern the system, and have had demonstrated utility in reduced-order modeling and control. Although numerous works investigating flow processes have implemented DMD, and similarly proper orthogonal decomposition, the results are often highly interpretive with little to no validation of their physical meaning. Additionally, a common result of DMD-based analysis is in capturing modal structures that are higher harmonics of lower frequency fundamental modes but have not been discussed at length. This work provides a focused study into the extraction of modes, harmonic modes, and their physical interpretation for common liquid injection systems. It is shown empirically that, for systems with suitable temporal resolution, standard DMD will produce harmonic modes even if higher harmonics are not present in the system. Only in specific conditions do these harmonic modes provide additional spatio-temporal information, but are more often indicators of system motion. Furthermore, DMD modes may be unable to resolve the underlying physical spatial scales whose dynamics they represent. Reasons for the emergence of harmonic modes are given.