When you voluntarily join the ballpit, you get a ballpit icon in the bottom-left hand corner. When you're placed there by an admin, you don't get the icon. It may be worth showing the icon whichever way you enter the ballpit, as some players have said they'd appreciate the icon whilst they're placed there temporarily by amen.
I considered this when I first implemented it and figured it'll likely confuse people who think they're there voluntarily rather than intentionally. One thing I exposed on the API recently that I plan to make use of is that users will be able to view their punishment history, current and old which would allow them to see if anything was wrong. We could try re-colouring or changing the icon if it's a punishment but I don't think the nuance would really be noticed.