Exactly, he removed all doubts from Nanjo's mind so now Nanjo's talking.
Nanjo POV next
I also think he appreciated the apology because it explained what Mokyeon was trying to do being all messy and manipulative to him. I also think deep down (maybe even on a subconscious level) Nanjo can sympathize with Mokyeon being so desperate for him because he's the same for Mokyeon, he's just more mature and less mentally ill and can disguise it better. His face in chapter38 when Mok, as he was confessing, said "what would you if you were in my shoes?" said everything IMO. He understands because he is feeling it too.
My theory(ies) is that what did it for Nanjo, is Mok Yeon talking accountability. Well more in terms of him being honest about his selfishness and his real intent from the beginning. Mok Yeon kept shifting blame towards Sunhwa and was being maniuplative towards Nanjo and disguised it as "trying to help Nanjo". (Maybe Nanjo also was aware of Sunwha's intent and was playing along)? When Mok Yeon eventually came clean, Nanjo could finally attack the "real" issue which is Mok Yeon's feelings and what they have going on + he must also like seeing crying Mok Yeon too.