I think if you dom them often enough (that is, where you're the one in control), it does make them more subby. To keep one of my slaves dommy, I made them a prostitute and offered myself to them, instead, as often as possible - unless I specifically needed to do something to make them level-up.
What I'll do is tell them to go boink inmates for monies, which places them in my cell and heading toward the prostitution spot. You can then just "Look around" to interact with them and offer yourself to them, assuming your attraction/etc. is high enough with them that they don't refuse. Repeatedly making an inmate dom you will make them more dommy over time.
It also helps if they're fairly dommy/aggressive, to begin with. They'll be a little more likely to misbehave when you want them to do something, though, probably. I find that I have to do "talk -> intimidate" in the slave dialog to get them to be more likely to cooperate, without straight up forcing or beating them.
idk if you put a bunch of restraints on them, if that will make them more subby or not. I don't usually put my dommy slave in restraints.