Logically, Alex being the boss makes way more sense than MC being boss does. She has the brains and knowhow, MC just has the muscle. It's natural for the children to take over from the parents in mafia organizations too.
Why would MC be made the boss over Alex? Boris will likely pick his daughter, not her daughters boyfriend. Unless he specifically doesn't want his daughter to be boss for her own safety.
And technically, Alex is already MC's boss. He was initially hired to be her bodyguard, not boyfriend. He still takes orders from her, when he needs to.