The vox-l simulator has limited functionality when it comes to displaying inventory, unfortunately. It's still in development, and in order to make the simulator load faster in everyone's browser (it uses alot of data), some of the functionality is pared down. So you may not see items 'appear' in your simulator inventory, but the badges should unlock regardless. Please let me know if they don't.
Afterwards, you can always test the inventory mods in minecraft -- they will work fully in minecraft.