Call-signs and three letter codes (such as QFA) are designated by ICAO at the request of the member state in which the airline is domiciled. If Tiger in Australia is going to be independent of the WSS operation of Tiger, then they almost certainly have their separate prefix and C/S. Who cares?
I understand that the call-sign assigned to an airline is used world-wide. Thus, Tiger should be using the same call-sign wherever it operates, and it probably is.
As for QantasLink, commercially they all use the Qantas two-letter code (QF) that is assigned by IATA. Their flight numbers are supposed to form part of a hierachy within the Qantas Group. Therefore, why should they use anything other than the operational prefix "QFA" and the call-sign "Qantas"?