As a Free action (post-errata), Blurred Step triggers after the action that triggered it is resolved.
Some definitions to start with:
Free Action Personal
Trigger: An adjacent enemy marked by you shifts
Effect: You shift 1 square.
Special: You can use this power only once per turn.
[Free Action] as reaction:
I'm playing a battlemind. If an adjacent enemy that I have marked attempts to shift to another square adjacent to me, can I use blurred step to shift to that square and prevent the enemy from entering it?
No. The free action granted by blurred step occurs after the action that triggers it.
Therefore, given that it is triggered after the action and not the movement the enemy moves, and then you move to follow, which preserves both the spirit and the wording of the rules.