"(who it’s alleged he started a relationship with WHILE still married to Mashonda)."

He had separated from Mashonda and they were divorcing when he dated Alicia. Mashonda herself later clarified this, after she stopped being as angry and in denial as she was about her years-broken relationship ending. Swizz had clocked out of that relationship several times, and had two kids with other women while he was actually with Mashonda, one before she married him. Mashonda should've ended it long ago but for some reason she wouldn't/couldn't. She then lashed out when she realized it was over, he formally separated and divorce was impending, and targeted the third woman, the most famous one, that he then dated.
When two people are separated, not emotionally, and divorcing, the only thing that makes them married is a meaningless legal piece of paper that is about to overturned legally when divorce is final. It's practically no different than someone who marries someone to get citizenship - they're only married on paper. When a person is separated and already dating someone else - they're not in the former relationship anymore.