This has me confusing pilots (me!) for as long as I've been around.
Here's my take:
"Alternate Minima" is the minimum ceiling and visibility required for the aerodrome to be nominated for use as an Alternate. It is published on the airfield charts if it is higher than the standard alternate minima.
It has nothing to do with destination landing minima and for obvious reasons is far more conservative.
An authority or company may specify a generic margin above a destination airfield's approach minima below which an alternate must be nominated.
If no alternate is nominated, once airborne you may continue to destination so long as reports (any) indicate it will be above the Approach Minima for the most likely approach around the time of arrival.
It the forecast changes its up to you just how much of a margin you want to apply to this. If it's going to be that bad at the destination then things are pretty screwed up and the logical course is to divert while you can.
In most countries it is not permitted to commence an approach if the actual VISIBILITY (either RVR or Visual range) is reported to be less than the Approach Minima for that specific approach. The exception is airlines that operate with an "approach ban" point (usually the outer marker or 1000' if no outer marker) where the approach must be discontinued if the required visibility does not exist.
This is written from a long haul perspective and things may be different in Australia (they usually are!).