I can see why you might be slightly put off by such a plotline. I'll try to explain it without any major spoilers, although as most of it happens in the first three or four chapters of the first book, it's not spoiling much.
So, two of the three focal characters in the series are a brother and sister who are British slaves originally from London. They get separated as children, and the boy winds up as the slave of a doctor, and for various reasons, makes him an incredible amount of money. As a result of this, the boy, Sulien, is treated with a great degree of leniency, and he and the doctor almost seem to forget that he is a slave. The doctor's daughter, Tancorix, is very resentful about this, but is sent away to boarding school for several years. When she returns, she's grown up considerably, and she and Sulien fall into a spectacularly ill-advised relationship - keeping this secret from her parents, of course. It's a consensual relationship, as much as such a relationship can be, but lurking at the back of it are all these years of unpleasantness and awkwardness: Tancorix's jealousy, Sulien inability to properly understand his position as a slave, and so on.
Tancorix's mother catches them, and before either of them can do anything, Tancorix is bundled from the room, whisked away and given no further opportunity to speak to Sulien or the authorities on her own behalf. The accusation comes from the mother, and it's depicted as an attempt to protect Tancorix's reputation. It doesn't play a great role beyond that, apart from getting Sulien in the right place, plotwise, to be a part of the main story of the series. The fact that he didn't quite understand what it meant to be a slave and owned by others is a major aspect of his characterisation, but the false accusation isn't central to this in the story.
For what it's worth, his sister, Una, has a way of knowing without a doubt that he didn't do what he was accused of (I don't mean she just doesn't believe her brother capable of such a thing, I mean she really knows without a shadow of doubt that he was falsely accused). She actually tells him that if she had found out he had raped Tancorix, she's not sure she would have rescued him.
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So, two of the three focal characters in the series are a brother and sister who are British slaves originally from London. They get separated as children, and the boy winds up as the slave of a doctor, and for various reasons, makes him an incredible amount of money. As a result of this, the boy, Sulien, is treated with a great degree of leniency, and he and the doctor almost seem to forget that he is a slave. The doctor's daughter, Tancorix, is very resentful about this, but is sent away to boarding school for several years. When she returns, she's grown up considerably, and she and Sulien fall into a spectacularly ill-advised relationship - keeping this secret from her parents, of course. It's a consensual relationship, as much as such a relationship can be, but lurking at the back of it are all these years of unpleasantness and awkwardness: Tancorix's jealousy, Sulien inability to properly understand his position as a slave, and so on.
Tancorix's mother catches them, and before either of them can do anything, Tancorix is bundled from the room, whisked away and given no further opportunity to speak to Sulien or the authorities on her own behalf. The accusation comes from the mother, and it's depicted as an attempt to protect Tancorix's reputation. It doesn't play a great role beyond that, apart from getting Sulien in the right place, plotwise, to be a part of the main story of the series. The fact that he didn't quite understand what it meant to be a slave and owned by others is a major aspect of his characterisation, but the false accusation isn't central to this in the story.
For what it's worth, his sister, Una, has a way of knowing without a doubt that he didn't do what he was accused of (I don't mean she just doesn't believe her brother capable of such a thing, I mean she really knows without a shadow of doubt that he was falsely accused). She actually tells him that if she had found out he had raped Tancorix, she's not sure she would have rescued him.
I don't know if that helps make things clearer.