Abstract We present an exploration of ∼500 spectroscopically confirmed galaxies in and around two large-scale structures (LSSs) at z ∼ 1 drawn from the Observations of Redshift Evolution in Large Scale Environments survey, an ongoing, wide-field photometric and spectroscopic campaign targeting a large ensemble of LSSs at 0.6 < z < 1.3. A sub-sample of these galaxies (∼150) was targeted for the initial phase of a near-infrared MOSFIRE spectroscopic campaign investigating the differences in selections of galaxies that had recently ended a burst of star formation and/or had rapidly quenched (i.e. post-starburst/K+A galaxies). Selection with MOSFIRE utilizing the H α and N ii emission features resulted in a post-starburst sample more than double that selected by traditional z ∼ 1 (observed-frame optical) methods even after the removal of the relatively large fraction of dusty starburst galaxies selected through traditional methods. While the traditional post-starburst fraction increased with increasing global density, the MOSFIRE-selected post-starburst fraction was found to be constant across field, group, and cluster environments. However, this fraction computed relative to the number of star-forming galaxies was observed to elevate in the cluster environment. Post-starbursts selected with MOSFIRE exhibited moderately strong O ii emission originating from activity other than star formation. Such galaxies, termed K+A with ImposteR O ii-derived Star formation (KAIROS) galaxies, were found to be younger than and likely undergoing feedback absent or diminished in their optically selected counterparts. A comparison between the environments of the two types of post-starbursts suggested a picture in which the evolution of a post-starburst galaxy is considerably different in cluster environments than in the more rarefied environments of a group or the field.