If the HOFD had someone spy on Mei and the mole in order to make sure nothing goes wrong, then why wouldn't they send someone to spy on Mei's killing (or lack thereof) of Jin - especially seeing as they know she has feelings for him.
Who says they didn't? It appeared to me they sent the jilted lover, Leo, to spy on them. Leo wanted Jin dead more than anyone. Zero danger of Leo getting a soft heart & letting them both ride off into the sunset too. HoFD also probably believed Mei & Leo were both very loyal given they both were willing to die for the HoFD & given their past tasks. Mei even stated she "knew" Leo would kill her for going with/after Jin, which implied she thought/knew she was being spied on.
Even if Leo didn't spy on them then maybe a spy we never see tells Leo. Jin needed to be dead if Leo was going to continue as an undercover spy.
After freeing Jin, Mei probably suspected Leo (the spy) would protect her with a fake excuse to HoFD & do anything for her so she felt safe freeing Jin.
Mei didn't immediately ride off with Jin, so Leo was probably hoping she was having a change of heart, she had her fling in the grass with Jin & maybe it was over now (maybe Leo was hoping Jin would be bad in bed too?). Leo would be the one waiting for her & there to pick up the pieces. When she went after Jin then Leo knew he had definitely lost her.
Mei was no match in fighting/assassination skills compared to Leo, which is why he is able to take her out so quick. If Leo had attempted to fight/kill Jin 1st then Mei could have arrived later & tipped the scales in favor of Jin as their battle lasted much longer.
Jin was probably right that Mei found it very hard to leave Leo & she felt loyal to him for saving her life many times in the past (& maybe promised him a future with her later while he waited for 3years? Leo seemed to really stress those 3years). After she sees Jin ride off & she thinks & ultimately decides how she wants to be free of being "a pawn" for HoFD & free from "forced" Leo despite her feeling like she owes Leo. She rides off taking a gamble that she might survive/escape when Leo attacks.