Hey there, I know this is not an answer to your questions, but are you referring to Society garlic/Tulbaghia violacea? Maybe what you are seeing popping up is a different plant?
I have always thought Society garlic is not invasive and have had the same 4 plants staying politely in one bed - only the clump is expanding in size but not popping up anywhere else. Maybe you have been invaded by the Allium vineale/wild garlic?
...or maybe I am just plain wrong in my thinking.
