We know that Russell Crowe is playing Dr. Henry Jekyll in The Mummy, a character who will be important in the larger Dark Universe that is being created around the classic monsters.
However, the movie is called The Mummy and you don’t want to get too bogged down in unrelated topics at the expense of the primary plot.
It’s unclear at this point how much of Dr. Jekyll’s backstory we’ll really get in the movie, on the one hand, the movie is setting up a larger world, and so a bit of world building is to be expected.
From all outward appearances Jekyll is being set up as one of the good guys, and Tom Cruise is clearly playing our movie’s hero, so if the two are fighting, we have to assume that it’s because Crusie’s character Nick Morton, isn’t fighting Jekyll, but his alter ego, Mr. Hyde.