McGivers is given the choice, to stay or to go. Admittedly, "staying" for her meant a full court martial. Khan's speech, as genuine as it is, does still seem to be giving her (for the first time?) the complete freedom to make the decision for herself..... but, seemingly, still imploring her to stay with him (or at least saying that he'd find it agreeable if she did). And when she does say yes, he talks of her admirably, but also possessively. She is "his". Perhaps he sees her as a spoil of defeat? He lost the Enterprise, but as a consolation prize he got the home version of the game and a complimentary busty redhead.
The script portrays McGivers as being generally weak in character. Submissive to the point where
any ancient despot could've been unfrozen on the Botany Bay and convinced her to obey him, not necessarily Khan. But of course, we are shown that she'd already been studying Khan, had painted his portrait. It'd be like a rock star you've loved all your life offering you a quickie in their dressing room before the show. Chances are good that you'd be tempted, and McGivers succumbed to that temptation.