We investigate how environment affects satellite galaxies using their location within the projected phase space of their host haloes from the Wang et al.'s group catalogue. Using the Yonsei Zoom-in Cluster Simulations, we derive zones of constant mean infall time \overline{T}_inf in projected phase space, and catalogue in which zone each observed galaxy falls. Within each zone, we compute the mean observed galaxy properties including specific star formation rate, luminosity-weighted age, stellar metallicity, and α/Fe abundance ratio. By comparing galaxies in different zones, we inspect how shifting the mean infall time from recent infallers (\overline{T}_inf < 3 Gyr) to ancient infallers (\overline{T}_{inf}> 5 Gyr) impacts galaxy properties at fixed stellar and halo mass. Ancient infallers are more quenched, and the impact of environmental quenching is visible down to low host masses (≤group masses). Meanwhile, the quenching of recent infallers is weakly dependent on host mass, indicating they have yet to respond strongly to their current environment. α/Fe and especially metallicity are less dependent on host mass, but show a dependence on \overline{T}_{inf}. We discuss these results in the context of longer exposure times for ancient infallers to environmental effects, which grow more efficient in hosts with a deeper potential well and a denser intracluster medium. We also compare our satellites with a control field sample, and find that even the most recent infallers (\overline{T}_{inf} < 2 Gyr) are more quenched than field galaxies, in particular for cluster mass hosts. This supports the role of pre-processing and/or faster quenching in satellites.