What is a “spectator mode” in this analysis of molecular vibration modes
The paper in question is Ab Initio Trajectory Surface-Hopping Study on Ultrafast Deactivation Process of Thiophene. From a quick Google Scholar search that returns 187 hits, it is clear that the expression “spectator mode” for a harmonic vibration mode is not a standard terminology, but is nonetheless used by plenty of authors.

As to the meaning, I think you got it from the everyday meaning of “spectator”: they are vibration modes that do not participate in the phenomenon of interest, i.e. that are not coupled to the chemical or physical process studied (which can be a chemical reaction, an adsorption process or a photophysical process).