Clay and future cubes anyone?

so apparently you cannot really turn off N.A.P.s in the game....I wanted to get this expansion pack but I do not want ballooning inventories in various homes that I don't play...makes me wonder if all the items being "stolen" don't end up in your neighbors inventories..this could be a issue not only from a game play point but in lag or how playable your game becomes over time. could someone please let me know if this is what is happening?