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Nope, they won't layer right. I tried researching it to see if it was something I did wrong in how I uploaded it and from what I could gather tileset B layers on top of A and tileset C ontop of B (and I'm assuming the same applies for D and E.) So in these examples the berries are on the same tileset as the trees so it's reading it as the same layer. (Same with the papers and the table in the art theme and I imagine anything else that's a single item meant to layer on top of others, like shelves and desks and the like.) I'll try to see if I have the tutorial I was reading saved and I'll share it here! 

edit/ Here's the article I was reading that breaks down the Letter sections for rpgmaker tilesets. It focuses on rpgmaker mv but its the same for vx ace as well. I 
https://medium.com/@robotsweater/bots-guide-to-custom-art-in-rpgmaker-mv-underst...

edit2/ I did a little more research and that link says the width of the sprite sheet for animated items has a width of 768 but that apparently will only work with MV, I tried putting in a sheet at that size and it didn't read it properly. For VX Ace it looks like the animated sheets have a width of 384, but the tilesets for the environment all have a width of 512. 

I hope that helps!