Seems like the terestrial types are like that. But usually the arboreals will not leave the cricket ball in their web if it is eaten in there, they will usually take it out of the web and drop it. The arboreals also will not usually poop in their webs.
My rosie has a designated area where she deposits her trash, sometimes she runs a dragline from her shelter to the dump site. Makes cleaning pretty easy. She does leave cricket legs and the occaisional head laying around just inside the mouth of the shelter and gets royally peeved when I pick them out with the tweezers. My A. seemanni buries its trash in the same corner and poops in another. I don't know whats going one with my curlyhair. She was in premolt when I got her but ate quite well for a few days and then went underground. She pooped in her water dish but I'm not sure where her trash is being deposited. She's not eating now since she has molted.