POP works by holding e-mails on the server until you want to read them, at which time the message is downloaded to your machine. This behavior is identical regardless of mail client, because it is determined by the protocol.
If you want different behavior, you need to either switch your existing accounts to IMAP accounts or get new IMAP-enabled accounts. GMail and your work e-mail will probably let you switch. With Yahoo you're stuck with POP unless you pay for their premium e-mail service.