Half of the Milky Way's baryonic mass is from other galaxies - when did this happen?
I think what you want to concentrate on is the bottom panel in your first figure, which shows the amount of accretion from different sources as a function of redshift (and thus time; see below). This shows that the contribution from "intergalactic transfer" (green cuve = material in winds outflowing from one galaxy that ends up in another) was almost zero until around $z \sim 3$ (age of universe $\sim 2$ Gyr), peaked at around $z \sim 2$ (age of universe $\sim 3.5$ Gyr) and then declined slowly from there, so that it's now about 10% of the peak rate.

"$z$" is the redshift, which is being used as a proxy for time: $z = 0$ corresponds to the present day (age of universe = 13.7 Gyr), $z = 1$ corresponds to an age of about 6 Gyr, $z = 2$ is about 3.3 Gyr, and so forth. You can use Ned Wright's Cosmology Calculator to convert individual redshifts to ages of universe (click on the "Flat" button to use a standard cosmology).

("Gyr" = gigayear = 1 billion = $10^{9}$ years, in case that's not clear.)