We present new analysis from the GEEC2 spectroscopic survey of galaxy groups at $0.8<z<1$. Our previous work revealed an intermediate population between the star-forming and quiescent sequences and a strong environmental dependence in the fraction of quiescent galaxies. Only $\sim5$ per cent of star-forming galaxies in both the group and field sample show a significant enhancement in star formation, which suggests that quenching is the primary process in the transition from the star-forming to the quiescent state. To model the environmental quenching scenario, we have tested the use of different exponential quenching timescales and delays between satellite accretion and the onset of quenching. We find that with no delay, the quenching timescale needs to be long in order to match the observed quiescent fraction, but then this model produces too many intermediate galaxies. Fixing a delay time of 3 Gyr, as suggested from the local universe, produces too few quiescent galaxies. The observed fractions are best matched with a model that includes a delay that is proportional to the dynamical time and a rapid quenching timescale ($\sim0.25$ Gyr), but this model also predicts intermediate galaxies H{\delta} strength higher than that observed. Using stellar synthesis models, we have tested other scenarios, such as the rejuvenation of star formation in early-type galaxies and a portion of quenched galaxies possessing residual star formation. If environment quenching plays a role in the GEEC2 sample, then our work suggests that only a fraction of intermediate galaxies may be undergoing this transition and that quenching occurs quite rapidly in satellite galaxies ($\lesssim0.25$ Gyr).