If I'm understanding what you're saying correctly, you're asking if in-game measure of your commander is changing the description based on personalities alone? If so then the answer is no, at least not completely based on that. I'm not an expert but I believe its based on a variety of things including current angst of the chosen, current broken vulnerabilities, etc. basically an overview of the entire situation at the moment compared to your current commander. Having trouble with the Significant Morality (Green) and Core Morality (Blue) it can be combination of tough personality matchup and less angst on them compared to the Minor Morality (Red), or your strategy focus for the minor morality needs to be different for the other two.
If you would like my recommendation, look at the angst between all three and note the differences, especially if you have a save just before you broke the T2's on the minor morality so you have a decent range to work towards. Additionally if youre trying the same strategy with minor morality on the others it would be a good idea to change that up.
For more help I would also recommend uploading a screenshot of your team's vulnerability so the people on the forum can give a more detailed tips than general ones like I have
A small addendum is some forsaken species with distortions allow you to capture flying chosen with varying drawbacks so I would look into that once you're more familiar with the game