Tshuos is the fact that we were spared. Milchamos is victory, that He fought our wars. We find these two by Bechoros as well. The Gur Arye explains that the Kedushas Bechorim is from being spared and the Pidyon is for the Bechorei Mitzriim.
The Ohr Hachayim Hakadosh says in Vayetzei that although Hashem pays back a person when an item was stolen and he didn’t deserve that, the pain of having been robbed remains. If the thief is caught then he is completely healed. This is what Yaakov Avinu asked for when he said Ve’asisa Imadi Chesed Va’emes. Emes is that he will have whatever is coming to him; Chesed is that he won’t have the pain of having been robbed.
The same applies here. By Chanukka and Purim the it was not a change of heart that stopped the Gezeira. We were Zoche to a real victory.