There still seems to be a misnomer that the fact that Khan would not be adversarial with his people as he was with the crew of the Enterprise is the source of the complaint. Like there's some perception that we expect him to tell every one of his lackies that he stabs at them from hell's heart, or throw them into a decompression chamber every time they come up to report that they've carried out his commands. :-)
But that isn't the issue. The issue is not that Khan is relating to people positively where he was relating to people adversarily in Space Seed. (Although I would still point out that his behavior toward Marla should be taken into account because that was someone he treated positively, in comparison, and his mode of relating was still very different.)
But no, of course Khan is going to be generous and gregarious and comradely with his people. The problem is the mode in which he does so. 
Again, to return to the metaphor of Kirk. We know that Kirk can be warm and comradely and friendly with his bridge crew. That's not a trait we see him display in every relationship, but with Spock and McCoy and Scotty, he most certainly can. But if the story portrayed him as being comradely and friendly with his subordinates by telling corny jokes to try and lift their spirits, or waxing poetic and starting to tear up about just how much each of them are his family and what they mean for his life (like a Discovery character of some sort), or grabbing them each a mug of ale and back slapping them while telling body stories and then getting into a bar brawl afterwards, you would say, that's out of character.  'But why?' someone could argue. 'Kirk is being comradley and friendly with his officers, it's within his character to behave that way toward them.' The point would of course be, yes, Kirk is comradley and friendly with his bridge crew- but not in that manner. There are still certain aspects of his character, ways he behaves, and that *way* of being comradley and friendly does not fit within them.
In a similar manner, the issue is not seeing Khan in a friendly mode versus only seeing him in an adversarial mode in the episode. That's never been the issue. The issue is that this friendly mode is completely lacking in any of the traits whatsoever demonstrated by the on screen Khan, and supplying traits that were not present in the on-screen Khan (from my perspective; subjectivity disclaimer). It makes sense that he would be friendly with his own people, yes. But it would still be the prideful friendliness of a dictator to his people. It would still be the haughty, superior, entitled man that we saw. Acting in a gregarious manner, sure- but we see him being gregarious (or at least aping such) in Space Seed and Wrath of Khan as well, in certain moments. There is still a grandioseness to it. A grandeur. A posturing. There's a *way* that he would be friendly. He isn't that way in the beginning of the story (before there would be any time for change). He is the way a completely different character would be friendly, and comradley, and all those other things.
And again, I recognize the freedom to disagree on those points! But the counter that he wasn't a mean dictator, he was a nice dictator, so he would be nice to his people misses the point; that was never the matter being argued. It's about the *way* he was a nice dictator to his people- and whether that way embodied any of the character traits that were at his fundamental core or not. It's not about behaving differently in different circumstances; it's about the core traits that underpin *all* circumstances (or at least, what is perceived as such).
And yes, maybe the 'gentler and more soulful' aspect is at the heart of it; maybe that's what I'm seeing as un-Khan-like and you're seeing as within a reasonable range for him.