I have grown up with doei my whole life. My parents and gransparents use for familiars and on the phone for bye. Dag is more a general use, but doei is more familiar, and used on the phone. If anyone speaks french they can relate this with 'salut' versus 'âllo', where the latter is purely for phones.
It's definitely correct, at least in Amsterdam, The Hague, Rotterdam and Leiden, where I'm based; it's just informal. I understand that it's considered too informal and even rude in other areas, and I wouldn't say 'Doei!' or its cousin 'Doeg!' after e.g. a job interview, but both are very common among contemporaries everywhere I go.