Generals Pemberton and Grant did personally meet to discuss the terms of surrender of Vicksburg; however, Pemberton refused Grant's offer of "unconditional surrender." At that point, Pemberton departed. Later, their subordinates met to arrive at the modified terms that eventually were agreed upon.
Grant sits on his horse early in the morning at an intersection and directs his army to march south, further into Virginia. As the troops march right to left across the screen, the rising sun is behind them in the east. That means the actors are actually walking in a northerly direction. The error is compounded by the actors/soldiers first muttering and then yelling "we are going south".