I also have had mold issues here in my rental house. At least four times my property manager sent the handyman to recaulk around the sinks where mold usually grew and still does. Right now caulk is wearing out again. WTF? The handyman replaced the bottom board of the cabinet under kitchen sink because of mold and sprayed the can of "mold killer/remover" on the sides inside. One time wood in the bottom of door jamb in the bathroom was gone around 5 inches high behind paint skin due to mold. Not even once we were asked to leave the place for a few days while he worked on them.
We don't want to move out because we love this place in a great neighborhood. Anyway I never had that problem when we lived in other places in different cities before. I told my property mgr about that. He said he also has mold issues in his place in the same city where I live so I asked if the city water has something to do with it. He said probably.