First something to note about Growing and Shrinking Mats.
Think about this as being similar to B and B+ borders. Growing places the mat outside the image and so makes the overall print larger.
However a "Shrink" mat retains the size of that specified for the image and is inside that envelope. Thus the aspect ratio of the image changes.
See screen shots below.
179 Grow setting
180 Shrink setting
181 Page editor crop tab showing how the aspect ratio has changed (red lines)
You can swop the setting at any time from the Photo Mats menu (right click)

The second thing I want to mention is about grouping.
Images and their mats are automatically grouped. In the Page Editor, simply select the outer-most mat and drag it, all mats inside that and the image will move together. If the image is selected, then that will move within the mat. The same applies to multiple mats - try it with say 2 mats, select the inner mat and drag, tha will move the inner mat and image together within the outer mat. Hope that is clear, as I said try it.  
See screen shot 182 below which shows the mat being dragged on a page with the image maintain its position with in the mat.

Terry