I know it's a given to question paradoxes in time travel stories, but how can she (from the present) pursue him into the past to prevent him from murdering her - unless they traveled at the exact same moment, her life would be at his mercy.

They both can only travel back to the same frozen moment in time, a world suspended in time. In that world, they both exist as frozen snapshots of themselves, and visitors from the future. To kill her in the past, first he must find where her frozen version is.

B A Mason Here's another version "When a tenacious detective discovers a serial killer is jumping back to the same frozen moment in time to commit murders, she must pursue him into a world suspended in time where a far graver threat awaits."