Its very simple. Zipmods are just zip files with their extension remamed that I dont think its even needed.
All you need to do is unzip the zipmod and move the abdata folder into that folder and zip it again then change the extension to zipmod, inside the zipfile there should be the abdata folder and manifest.xml but this isnt a 100% system ... Xyth24 files dont work that way for two reasons, they dont have a manifest.xml or even a zipmod to begin, this isnt much of a problem were its a extra step but the main problem is the list folder, he uses unity3d files as zipmod seem to only work with it being .csv files.
It seems your problem is you are only using the zipmod files and not moving the abdata folder, this have to be done for EACH mod if it bothers you that much ... if you move the abdata folder to the game root folder it will work, its really just a organization method since uninstall "hard" mods is much more annoying as you have to do to the abdata folder and delete those files and some moders use the same files across mods so you could delete a file you need.