We have employed emission-line diagnostics derived from DEIMOS and NIRSPEC spectroscopy to determine the origin of the [OII] emission line observed in six AGN hosts at z~0.9. These galaxies are a subsample of AGN hosts detected in the Cl1604 supercluster that exhibit strong Balmer absorption lines in their spectra and appear to be in a post-starburst or post-quenched phase, if not for their [OII] emission. Examining the flux ratio of the [NII] to Halpha lines, we find that in five of the six hosts the dominant source of ionizing flux is AGN continuum emission. Furthermore, we find that four of the six galaxies have over twice the [OII] line luminosity that could be generated by star formation processes alone given their Halpha line luminosities. This strongly suggests that AGN-excited narrow-line emission is contaminating the [OII] line flux. A comparison of star formation rates calculated from extinction-corrected [OII] and Halpha line luminosities indicates that the former yields a five-fold overestimate of current activity in these galaxies. Our findings reveal the [OII] line to be a poor indicator of star formation activity in a majority of these moderate-luminosity Seyferts. This result bolsters our previous findings that an increased fraction of AGN at high redshifts are hosted by galaxies in a post-starburst phase. The relatively high fraction of AGN hosts in the Cl1604 supercluster that show signs of recently truncated star formation activity suggest AGN feedback may play an increasingly important role in suppressing ongoing activity in large-scale structures at high redshift.