The creature's ability to raise the dead that it uses to animate the Cossacks seems to come out of nowhere... until you remember that it was doing exactly the same thing right at the start of the movie when it was still inhabiting the mummified corpse. There seem to be some unclear limits to this ability, however (as the creature abandoned other dying hosts instead of animating them; however, all hosts it abandoned had been wounded by attackers, while the mummy seems to have "merely" frozen to death and decayed a little. Perhaps the ability only works on those who are fully dead).
It is conceivable that the creature did not jump host from the mummy to the inspector until the mummy was shot because, once reanimated, the mummy no longer counts as dying, and thus the creature cannot voluntarily leave.
And apart from dying still hurting, the creature probably isn't eager to mortally injure itself voluntarily in order to jump to a new host, especially if there is always a risk of the prospective host managing to avoid eye contact if the creature's current dying host becomes too weak to force its intended host to meet its gaze.
The mummy the creature inhabits at the beginning of the film only has one eye left. If the creature can truly only move from one host to another when making eye contact, it was that close to being rendered permanently dead, which is probably what is finally accomplished by smashing its host in the crashing locomotive and burning it to ashes in the ensuing fire.
