He was not incarcerated at all after his encounter with Potiphar's wife. He was merely transferred! Potiphar was in charge of that jail, remember, he was an employer and Yosef was already in his service. He'd put Yosef in charge of his household but Yosef chose not to give in to the wife.
Think about it. This is Egypt, affluent and probably to some degree decadent, as affluence usually brings this tendency . Nobles had time on their hands and they weren't exactly living the same ethical code as Yosef's family back home in Canaan. Furthermore, if Potiphar was indeed a saris, in the full sense of castrated servant of Pharaoh, what would be the understanding? A very good looking young boy employed within reach of the idle wife? Does anyone really think in such a situation he'd be expected NOT to resist? It's the concept of 'boy toy' and it's ancient. Potiphar expected the situation. He wasn't worried about bringing in an adulterer, he was a saris! He was providing entertainment for his wife. Yosef's compliance to the situation was expected. The text says Potiphar withheld nothing but the bread he ate. Interpreters say he means his wife. I think we can take it literally. He was NOT withholding his wife and neither did she expect to be withheld. She certainly wasn't expecting Yosef to withhold himself!
Look at her reaction when Yosef resisted her. Did she charge him with rape? Attack? No, those were NEVER the charges. Look at 39 :14 and following and read it with this understanding. What is 'letzahek bi' ? It's based on the verb to LAUGH. Some of its meanings are associated with immorality but NONE with rape or assault. No language of INUI (such as is used with Dina and Schem) If you take it as immorality she's saying 'he was brought here to have (sexual) fun with me!' That was the purpose! If you take it more literally, it's 'he's mocking me!' by refusing. Nowhere does she complain that she was molested, assaulted or otherwise approached in a very naughty and unbecoming way. Would that even be believed as a protest if everyone was expecting that to happen?
This situation was at most embarassing for Potiphar but he did not wish to lose Yosef's acumen. It was more of a 'shrug, that didn't work out, too bad for the wife, oh well, I can use him somewhere else.. I know, he'd be good in the jail, he can help the wardens, he has organizational skills!' Well, as we know he soon had the trust of the wardens and was pretty much running the place very soon. They also liked him and recognized his abilities and charm. Do you really think that could have happened if he had ever been locked in a cell? He was never incarcerated! This is how he came to know both the baker and the cup bearer, who probably weren't even in the same cells because he was helping run the place from the start.
Our assumption that Egypt would treat Yosef's alleged assault on Potiphar's wife is cultural, psychological projection on our part. We try to apply our way of looking at morality on Egypt but their approach to these issues was far more liberal. Potiphar's wife simply could not relate to what she would see as prudishness in the extreme. She was merely trying to get what she took for granted as hers and stunned that he wouldn't go along with it. After that a transferral to another office would be Potiphar's most logical move.
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Of course Yosef wasn't taking REVENGE on his brothers as some modern interpretations suggest. This is offensive! A person taking revenge gets satisfaction out of it. He'd be practically rubbing his hands together in glee over the next mindplay. Yosef could hardly keep himself from weeping. He went into another room to cry over the whole process but wanted to see it through, wanted to be sure where his brothers were holding, regarding himself, what they'd done in the past, their relationship with their brother Binyamin, their relationship towards money and honesty in general. He wanted to think the best of them. He wanted to discover that they were virtuous. It is far more wonderful to find out that someone is better than you think they might be. He wanted that, wanted very much for them to pass all the tests he set them, to be sure of them before he'd reveal himself, if he would. It was very painful for him.
Why, one might ask, did he put his father through the grinder too? What had his father done? Why make his father send Benjamin?
This was not to punish his father but, I think, in order that his father overcome his own fears. This is the place of the parent eventually, to stop trying to protect one's young when they come of age and send them out into the world. Of course anything might happen but that should be allowed to paralyze anyone into regressive behaviour. Yaakov's situation was special of course. He had a great deal emotionally invested in Yosef, he believed him torn by a wild beast and was inconsolable. He never could see or bury his son's body and so never had any real closure on that. Perhaps somehow he also intuited that his son was still living and this tormented him subconciously. I think the parents of Ron Arad and other such M.I.A.s must have gone through something as terrible. He was understandably resolved not to let the same tragedy happen to Binyamin, though , as we see, he had no qualms about sending his other ten sons all the way down to Egypt.
Yosef knew as long as Yaakov would hold onto Benjamin for fear that he would be lost, like his brother, the more neurotic he'd become. That fear and neuroticism would also transfer to Binyamin and tend to make him somewhat timid and paranoid. Obviously an unhealthy situation which MUST be avoided. No. Yaakov must face his fear of losing Benjamin, he must take the risk. He must have faith. Here Yosef concealed his real identity from his father, long distance, so that Yaakov would be forced to let go of Benjamin and deal with facing those risks. This was an enormous test of Faith for Yaakov and without nevuah, because of his loss of Yosef, he was really very much in the dark as to what would be. It was still necessary and this was clear to Yosef. Yaakov also had to recognize that he was treating his sons on a double standard. Was Benjamin in reality worth so much more than his brothers that he will fear for one and not so much for the other? When would Yaakov finally get past his disastrous preferential treatment?
This all caused Yosef further pain, and he was obviously concerned that his father might not even survive these strains. This is why , he had to ask AGAIN 'is .. father still alive?' His brothers had already told him their father lived! So painful for Yosef, who cannot restrain their tears when the final revelation is made! For me this is the most emotional parsha of Genesis, of the whole of the Torah in fact.
These collossal tests of faith are pivotal to the entire future of the Jewish people, both spiritually and in simple historical terms. That is a whole other topic well covered by many writings, and I really hardly have anything to add there but it is obvious and clear that it is so.