A37 The extra damage applies immediately when the hit target moves, no matter what weapon you are using.

If you happen to hit with one of the special weapons for this attack, you get to shift 1 and slide the enemy right when you make the attack (this does not require a move action on your part). Your shift and slide does not require the target to move and take the extra damage (they wouldn't have had a chance to, because this part of the power only applies immediately after hitting). If you shift and slide them, and they, before the end of your next turn, move from the square that you slid them to, they will take the damage as described above.

I'll agree the wording on this power might be a little odd, but I believe the reading I describe above is consistent with the way other powers with similar wording work.