Brett,
Good of you to join us at this SE forum - welcome
I should confess the physical properties is not something I use regularly.
I have not had the same problems as you have,
neither in the part nor the assembly enviroment.
This was tested under SE V18 service pack 5.
(Help -> About -> version=18.00.05.05).
I know there is some 3rd party programs that can extract this type of info from your assemblies and parts without even opening the file yourself.
Assume that the process is done manually - by opening the file and asking for the calculations to take place.
I did the following:
1] created a part in SE part enviroment
2] selected Inspect -> Physical Properties
3] a pop-up window comes up showing the physical properties
4] the density should be set (LEFT) to the correct material / value
5] the UPDATE button (LEFT, BOTTOM) should be pressed to update the part
6] RIGHT TOP values for
...........[a] mass,
...........[b] volume,
...........[c] surface area
7] RIGHT MIDDLE co-ordinate values for
...........[a] centre of mass (red circle)
...........[b] centre of volume (green circle)
>> if ticked to show, a green / red circle is shown on the part
8] Mass moment of inertia is also shown, RIGHT BOTTOM
The same process were repeated on an existing assembly.
It was not tested for the "plate" enviroment.
Note that if the same material type is used for all parts within an assembly,
the centre of mass & centre of volume will be in the same place.
Only if there is a difference in materials, there would be a change.
Also make sure that all parts within the assembly is actually the right material.
I know my friends many times do not bother to set the correct material types.
That would influence the accuracy / correctness of the calculations.
Please come back to the forum and tell us if it was helpful.
Maybe try to explain again what the problem is, if it was not of help.
Your

CAD friend,
WB