Sorry that you're having an issue here. It would be great if one of the forum admins can get some more info from you on the issue. As it would be good to have the team take a look at why you got some "phantom" voicemails in the web client.
As to deleting voicemails, it depends... If you're using say the native voicemail app on the iPhone or another device, then the DIGITS ecosystem doesn't necessarily know that you've deleted it since it's at that point stored locally. If you delete it from the DIGITS app, then it would be deleted across the board.