Son suffered Asian Cup disappointment with South Korea on Tuesday as they lost 2-0 to Jordan at the semi-final stage.
The South Korea skipper cut a dejected figure at full-time, but was quickly back on a plane to the UK and trained on Friday to make himself available for Spurs' fixture with Brighton.
Postecoglou said: "It wouldn't surprise anyone to see him be like that.
"He was very, very disappointed with Korea's exit because they haven't won it for quite a while and after they got past Australia, when you get to the semi-final stage, you feel so close.
"But anyone who watched the tournament knows he gave everything for his nation and didn't leave anyone questioning his commitment to his country.
"He was spent by the end of it but I spoke to him not long after it and he was keen to come back, get amongst the boys again. He was keen to come back here.
"It didn't surprise me that he wanted to train straight away and be available. That's why he is the person he is."
Bissouma endured a mixed Africa Cup of Nations campaign with Mali after he struggled with illness, but Postecoglou explained: "Yves had a slight form of malaria before the tournament started, but it cleared up after the tournament started. He had no issues after that."
Postecoglou is excited to have his options in midfield and attack boosted ahead of the final three months of the season.