Our SAS had some Tikkas in 22/250 for urban use in the '80s but until now I've never heard of the OZ army playing with a 223 DMR.
As an aside, I use a Tikka T3 223 out to 800m in our Precision Service Rifle competition firing 80.5gn Berger Fullbore projectiles @2940fps and they behave exactly as would the 155gn Dyers out of a 308.