Had a collegue of mine help me figure this out... I was having the same issue.
The leader connection to the point is not set in the style. It's per point. Select a point, go to properties, Under Annotation heading, Leader Attachment Option, Select Point - instead of Marker Extents or From Marker Style.
This will force the leader to the point coordinate. To do a mass selection of points, click a point, right click, hit select similar, then change in properties as stated above.
NOTE: I believe that the Leader Attachment Option from above called From Maker Style is confusing, because points do not use a Marker Style, which is an actual style in Civil 3D. They use a point style for their 'marker', in which to add more confusion does not have any settings for leader attachment. I believe that both Leader Attachement Options (From Marker Style and Marker Extents) use the extents of the marker object to calculate the end of the leader.
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