Japanese princesses dont have innate approach behavior. The best that can be managed to to speak when spoken to a bit more often and possibly even letting someone send a note in response, but usually not directly from the princess herself. If she is extreemly interested, she might make a small noise but that noise will stop as soon as any movement or statement lets her know she was heard.
So how did japanese princesses have so many children by commoner men? Well, they arent as intimidating as princes and emperors, so they dont contain themselves as much. If the man is curious about what he overheard he might find a way to get in.
Once is always forgiven of the princess, especially if no one ever finds out. But some of them get tired of the necessity to maintian non approach behavior after the cat is out of the barn and start making a lot of noise around commoners.
So how do princesses have children by princes and emperors? They hear about them, notice their skills, like their looks, then take matters into their own hands, and if the princess ever takes a liking to what is happening it works, if not it doesnt work out. Many of the princes and emperors have the ability to bond women to them for life even if they didnt have any interest in them before they were raped by them. These men usually know better than to expose commoner women to this power basicly because doing that to japanese women and then leaving them behind leads to homicidal behavior, or atleast public embarasment.
You might notice in literature that the princes and princess have high expectations about how they should handle their romantic affairs. These restrictions get lighter in successive generations usually because the ability to own people through having sex with them is deliberately being bred out before they are released on the general population, however due to the indiscressions mostly of the princesses, these genes have gotten into the general population.
