Hi,
the Catalyst system provides heights on the ellipsoid - so not on any Geoid.
A difference of around 40m smells like a Geoid.
If I may ask - which software did you use for collecting the data and which config did you use. If I search the EPSG databse for GDA 94 Zone 56 I get essentially this:
EPSG Geodetic Parameter Registry (click on 'retrieve by code', then use code 28356).
So the GDA 94 Zone 56 is a mix of geodetic datum and none default height model (EPSG::6422, Ellipsoidal CS).
My GUESS is that this causes the offset.
To give a better answer we need details on the settings as applied in both the application and Trimble Mobile Manager (used datum etc).
Regards
Nico