Are airline ICAO codes unique?
ICAO three-letter codes are always unique. The official source, ICAO Document 8585, says the following:

1.2 The same designator will not be registered for more than one aircraft operating agency, aeronautical authority or service.
1.3 No more than one three-letter or telephony designator will be registered for each aircraft operating agency, aeronautical authority or services.

In your example, Tiger Airways Singapore only exists as a single airline in document 8585. The fact that they have an Australian division does not mean that it is a separate aircraft operator, and thus no separate ICAO code can be assigned.
You can find more rules regarding ICAO identification codes, including a complete list of every ICAO code in the world, in doc 8585: http://dcaa.trafikstyrelsen.dk:8000/icaodocs/Doc%208585/DOC%208585,%20Edition%20no%20149.PDF
Interestingly, British Airways seem to contradict the above rules with their seasonal &quot;Santa&quot; flights. Around Christmas, certain British Airways flights will operate with the XMS ICAO code (radio callsign &quot;Santa&quot;), instead of the usual BAW ICAO code (radio callsign &quot;Speedbird&quot;).
In ICAO doc 8585, the XMS code is registered to &quot;British Airways Santa&quot;, which I very much doubt is the name of a real company, so it does seem there are ways around the rules quoted above.