If so, how did the US manage to reimburse such a large group of people?
I apologize for the brevity in advance, but I don't know how to stretch this one. No, they were not able to do so - the money just became worthless. Many people and institutions (such as universities and colleges) that had invested heavily in Confederate war bonds were ruined by the collapse of the Confederate government. This is part of (along with the huge loss of capital in slaves) why the South remained economically depressed for the next hundred years or so.