House positions definitely have a psychological influence, but mostly they are just general indicators of physical environments a person ends up experiencing.
For example, Sun in the 12th is said to be one of the classic positions for someone ending up in prison...according to the old texts. What it means in modern society though is that the person ends up somehow working in isolation...kind of like being in an "allegorical" prison but not in reality.
I have a 12th House Sun, and my career often leads me to work behind the scenes of large projects. I'm highly key to the projects, but few people know about me. I also work at home alot with fairly little interaction with others or supervision. At the same time, my Sun is Sagittarius...is fairly outgoing. You'd think they'd conflict, but they don't...for me at least.
The 12th House Sun doesn't really give you conflict in of itself. The Sign position will blend with the House position psychologically speaking, to the point where you'll start preferring to work on your own.
The 10th House Moon seems like it might cause an inner tension, but the 10th and 12th Houses are in Sextile relationship. They don't fight each other. I find the Moon in Leo in 10th highly comfortable, provided there aren't hard aspects to it. Probably what it means is that you'd make a comfortable public persona, but your real work to appeal to that public is something done intensely in private before presentation.
I wouldn't look for psychological tensions here. If you have them, they likely aren't a result of a 12th House Sun and 10th House Moon. I'd look to the position of the lord of the 12th (in the sidereal zodiac) to find hints where the native ends up working in solitude.
