I’m away from my computer for a week or so, but from what I remember I think you can select the transparency color in RPG maker when importing the sprite sheet. So you would select the green background as the transparent color.
Apologies that I can’t be more helpful at the moment.
For RPG Maker as an engine, this asset pack is compatible with VX Ave. Are you using a plugin to get this to function correctly with MZ? I've uploaded a new version of the pack that contains tilemaps with transparent backgrounds in the 'RPGMakerVXAce' folder.