I have a Gmail account (gmail 1), and if I'm moving email from Inbox to an IMAP folder, the email disappears from Inbox and after changing the folder and going back to Inbox the moved mail is back in my Inbox.
I just created a new Gmail account (gmail 2) and tried it with this account. The behaviour is like expected: moved emails don't re-appear in their old folder.
Now, I don't know how to fix this. I've checked the account settings from both accounts, the new one and the old one and I can't find a settings difference to fix this problem.