ID:1978922
 
Not a bug
BYOND Version:509.1313
Operating System:Windows 10 Home 64-bit
Web Browser:Firefox 41.0
Applies to:Dream Maker
Status: Not a bug

This is not a bug. It may be an incorrect use of syntax or a limitation in the software. For further discussion on the matter, please consult the BYOND forums.
The layering breaks when using the SIDE_MAP format if you animate() a mobs pixel_z. The bug report is pretty vague, but I've included a test case and should be extremely straight forward for you to understand.

Run the project. Move around a bit. You'll see the layering is fine. Then click the Jump verb. Now move around again, it seems the layering breaks.

https://www.dropbox.com/s/lmc8c3dhyo8tftt/Test.rar?dl=0
In the test project you sent, the jump isn't actually jumping properly. You increase pixel_z to 12, but then you decrease it to -12, lower than it initially was.

Once pixel_z is negative, the mob appears beneath the row of turfs to its south, which is correct behavior because it's actually not "on" them in terms of its physical footprint. If you visualize each tile as a cube where you're seeing the top face at an angle--which is how SIDE_MAP is intended to work--the mob is definitely behind the object to its south.

[edit]
I forgot to mention, when the pixel_z resets to 0 at the end of the jump like it should, the mob does not partially disappear behind another tile.
Lummox JR resolved issue (Not a bug)
Oh crap, ha! Whoops! Didn't realize I did that.
No problem. Thanks for posting a demo; it made this much easier to look into. SIDE_MAP does have its share of layering issues, and will until I eventually get to a true topological sort.