Can you show a screenshot of the shifting?
Will the layout be changed, if you open the exported IDML in the same version of InDesign where it is exported from?
PS. Ther is no easy way to prevent this.
Just possible ways to store information about position of every frame "inside" the page items and a script that can try to recreate these.
What version of InDesign do "they" run?
Can you show a "before" / "after" after doing a "Select All" also showing the frame edges and the "links" of possibly threaded text frames? Also show "Hidden Text".
Ask for a screenshot from "them".
Something like that:
PS. Edit: Could not insert screenshot from my inbox here in the forum…
Now the screenshot should be visible.
If you’re on CC and they need CS6 then you should install CS6 and work on that. Why fix something when you can avoid it?