  We illuminate the altered evolution of galaxies in clusters compared to the
field by tracking galaxies in the IllustrisTNG300 simulation as they enter
isolated clusters of mass $10^{13} < M_{\rm 200, mean} / {\rm M}_\odot <
10^{15}$ (at $z=0$). We demonstrate significant trends in galaxy properties
with residence time (time since first infall) and that there is a population of
galaxies that remain star-forming even many Gyrs after their infall. By
comparing the properties of galaxies at their infall time to their properties
at $z=0$, we show how scaling relations, like the stellar-to-halo mass ratio,
shift as galaxies live in the cluster environment. Galaxies with a residence
time of 10 Gyr increase their stellar-to-halo mass ratio, by around 1 dex. As
measurements of the steepest slope of the galaxy cluster number density profile
($R_{\rm st}$), frequently used as a proxy for the splashback radius, have been
shown to depend strongly on galaxy selection, we show how $R_{\rm st}$ depends
on galaxy residence time. Using galaxies with residence times less than one
cluster crossing time ($\approx 5$ Gyr) to measure $R_{\rm st}$ leads to
significant offsets relative to using the entire galaxy population. Galaxies
must have had the opportunity to `splash back' to the first caustic to trace
out a representative value of $R_{\rm st}$, potentially leading to issues for
galaxy surveys using UV-selected galaxies. Our wok demonstrates that the
evolution of cluster galaxies continues well into their lifetime in the cluster
and departs from a typical field galaxy evolutionary path.
