The shape of the curve is due to the dispersivity value when solving the ADE. The dispersivity value incorporates both diffusion and physical dispersion. The more vertical the curve, the smaller the dispersion, the more horizontal the curve, the greater the dispersion around the center of mass. The center of mass (center of the curve) is exactly the advective flow velocity. In plug flow you would have misible displacement and essentially a vertical front with the injected fluid displaying the initial fluid. There might be a slight spreading (the curve would not be perfectly vertical) due to diffusion. You might wish to try the simulation without any sorption first to confirm this.
In your example I believe the curves are inclined upward because the center of mass has passed through the column in the last two time steps you plotted. In effect your solute has accelerated near the column's end because there is no longer any retardation (sorptive capacity overwhelmed -you can verfiy this by plotting sorped fraction) and you are seeing plug flow with a slight reduction in inlet concentration due to mixing between inlet and initial fluids. If you kept running the inlet fluid through the column it would eventually completely displace the initial fluid and the solute concentration at the end of the column would be equal to the front of the column (new inlet fluid). It may help to think of the last two curves as the trailing edges of a plug flow example with very limited reduction in the solute concentration by sorption.
My solution was to increase the sorptive capacity to maintain the curve shape meaning the shape was a function purely of the dispersive term in the ADE. Of course, this also has the effect of slowing the solute transport since the retardation is now constant throughout your simulation time and may have confused the issue. It may be helpful for you to add a conservative tracer to your inlet solution so you can compare the transport of both and see the difference.
Sorry if I did not make this clear in my first reply. As to a better person to explain this to you - you can try Dr. Bethke or perhaps Dr Fetter, although I would review Fetter's Contaminant Hydrogeology text before asking him. You can also try an analytical solution to compare with the model.