I'm glad you came out ok.
However I do buy and own a lot of those cheapie chinese plug packs, I think shipped to the USA it cost me $1 each delivered.
It may be a problem if you are just a consumer, but if you have electronic skills, these are a bargain, its like hunting for reject parts from a factory, or salvaging components from the trash.
Like Dave, you should take it apart to know what you get, so when you buy them get one that is screwed together, rather than glued.
You'll find many of them are decently made, no worse than if I made it myself as a DIY kit, but I would be hard pressed to get the casing and wiring as ergonomic, or even the same parts for $1.00. Just the postage alone shipped from China would be more than $1.00. However, like many things I get from China, even better made or more costly, seem to lack something here and there, that if they just added, would up the quality quite a bit.
For plug packs, many are not fused, so if they short your circuit breaker is your main protection against sparks and possible fire. If you are skeptical, just use these plug packs through a power strip or surge protector, which has the circuit breakers that can trip for you before the mains line.
With the right equipment, you can test the specs of these AC-DC converters and add the parts needed to improve regulation, ripple, and protection.
Derate them, if its rated for 1A, only use it to 500mA, for example. To insure you remember, fuse it with a much lower rated fuse than its operational capacities.
For what you just experienced, and I have plug packs that look just like yours, don't pull the pack by its adapter, as you've already found out, because the terminals could still be in contact in your hand, disconnect the pack separately or glue or zip tie the adapter permanently to the unit since it looks like it has USA style plug, and you need the Aussie one.
If you buy brand name items direct from China, they could be counterfeit. All the labeling should be considered meaningless without prior testing. You may pay extra for a fake brand name, but don't get the same quality control or reputation; you're better off getting the no-name and checking its specs.
If you know what you pay for, and can troubleshoot it, its not a bad deal.
Lastly, beware of chemical contaminants in the product itself. Since these are not made to be eaten or placed in your mouth like toys or food, its less an issue. If this worries you, just wipe it down with ethyl alcohol before you use it, that should remove all the superficial ones that you might get on your hands.