...heh. The "lock and key" metaphor isn't the best; I apologize if it's confused you. Perhaps the best way to think of it is to think of Actions and Decisions. Do-er characters prefer Actions, and Be-er characters prefer Decisions. Remember also that Do-ers and Be-ers see their personal problems as entirely different things. For example, say the MC has cancer. To a Do-er, this is a Universe problem, because their physical body is now in danger of swallowing them. But to a Be-er, the problem isn't the cancer, but their fear of death. Sickness, injury, cancer--these things come and go. To a Be-er, their need isn't to cure their cancer, but to change their mentality until they can face death with a smile.
As to your question. This is kind of the thing, isn't it? You have to do things to change the internal, and you have to be a certain way to change the external. You have to be careful with the words, because they mean a specific thing in Dramatica terminology. So for example, doing favors for your friends to make them like you better is actually an Internal, Be-ing action, not Doing; specifically, it's about Playing the Role of a good friend, which is under Manipulation/Psychology/Ways of Thinking. Yes, it's about affecting someone other than yourself, but it's about affecting their minds, their internal selves.
Have you ever heard of the game Psychonauts? The important bit is that basically, the characters can step into the brains of other people, and their emotions and hang-ups are depicted as real, physical objects. When you write a throughline with an Internal Domain, imagine that the story is literally taking place in a world like that. Imagine the roles people play, or their beliefs, or their fundamental natures, as mental objects, and the conflict of that throughline is about the characters interacting with those objects. Zootopia has an OS of Mind--imagine the stereotypes of carnivores as a big hulking psychic monster, and each of the characters do their part to either defang or strengthen the monster. Nick Carraway's MC Domain in The Great Gatsby, on the other hand, is in Psychology--specifically, Becoming. For this one, we need to imagine Nick's self-image as a big old Jenga tower, and the story is about him plucking out those pieces one by one.
So in your "leaving the city" example, it depends on what the problem is. If his problem is in Universe (for example, moving out to the Radio Quiet Zone so he stops getting headaches), then what he's doing is an external action to affect the external world. But if his problem is in Mind (for example, moving out to a log cabin to weaken his love of earthly pleasures), then he's performing an internal action to affect the internal world. The point in the second example is not that he's changed physical location, but that he's cutting off the source of his desires.
...I have no idea if I'm making any sense here, or if I'm just coming up with silly illustrations now.