First of all, I dont think Jogi has any 'murderous past'. Whatever happened was an accident, its not like he purposely murdered Ichcha's father. To top it off, Pushkar had a major hand in her father's murder as well. Jogi's done everything he can to try and repay Damini. Even though money can never bring back what Ichcha lost, atleast he tried to fill the hole in her life.
I'm not saying he didn't make his share of mistakes though. His number 1 mistake was not spending enough time with Tapasya and getting to know what sort of person she was starting to become. If he had, maybe he would have been able to stop what happened. His next mistake was actually BRINGING her back from the hostel. Tapasya leaves Ichcha in the forest, where almost anything could have happened to her, and she gets no punishment? Maybe if they had left her in the hostel, or atleast been stricter with her when she returned... then she would have been a lot different.
And I dont think Damini/Ichcha can be considered as 'strangers' for Jogi and his family. They've practically been living there for 10+ years and have done so much for them. Damini would never have had to become a servant if not for Jogi's mistake, and he knows that, and he's trying his best to repent for it. I'm sure Jogi knows Ichcha well enough to know that she wouldn't have walked out of this marriage unless pushed, and his different attitudes towards Ichcha and Tapu are completely understandable. And I'm extremely happy with Jogi's behavior towards Tapu, its the best punishment she can get for what she's done.