What you see in preview should be pretty much what you get - if MATCH MONITOR mode is chosen. But even if MATCH CONTENT is the choice, the image should not move vertically when exported. If there's a difference between VP preview and the exported file, it could be a monitor issue. Have you tested another monitor?
As to effect placement: Effects can be animated. Keyframes (represented by dots) can be set for IN/OUT times ... and to track a moving image, if necessary. As the subject changes position, drag the effects window scrubber (red line) to the new position. A new keyframe should be automatically set. If not, click the green + sign.

Here is an in-depth look at how to animate.
Share your project and someone will check it out.
Here's how... http://nch.invisionzone.com/topic/23659-tips-for-getting-help-on-this-forum/
If it contains sensitive material you can link it in a personal message (PM) to me, via the envelope above. Be sure to FILE|SAVE PORTABLE PROJECT AS, not simply SAVE PROJECT, and don't forget to share it.