Response of First order circuit to a pulse input
The pulse starts at t = 0 and ends at t = T. And you're trying to find the response after the pulse ends. 

First you solved for the response during the pulse, so you know the capacitor voltage at t = T. Now you want to find a response starting at time T. You're basically solving a whole new problem starting at time T, using the previous calculation to tell you the "initial" conditions at time T.

So the problem (and solution) is "shifted" in time compared to what they probably taught you previously about finding a response starting at t = 0, given initial conditions at t = 0.