The welcome scene and the departure scene, as you call them, are sort of mirror images of one another. They show how the fortunes of the speaker have been turned completely around in the year that elapsed between the two scenes.
In the welcome scene, the speaker is a hero. The people are all praising him. They would give him anything he wants as he is paraded along.
In the departure scene, he is being paraded again. But this time his hands are tied and he is clearly about to be executed. This time, people are throwing rocks at him.
Over the course of the year, he went from a hero to a villain, presumably because he did not achieve the goal he set out to achieve.
In the beginning of Robert Browning's poem "The Patriot" the departing scene shows the popularity and excitement of the moment. Everyone celebrates and presents the person on a pedestal. He is exhausted for his effort.
However, as the time goes on, the popularity of the event wanes. The patriot becomes the forgotten. It doesn't matter that he is doing his duty in the rain soaked roadways.
Towards the end of the poem the people have turned on the patriot. There is no more fan fare and he is all but forgotten. In the end the same people who had worshipped the patriot are now ready to have him executed. The crowd has gone from one that had admired the patriot to one that detests him. His popularity has waned.