It is worth distinguishing two issues: anger that another country applies its laws to one of our citizens; and anger that another country (any country, actually) applies unjust laws to one of our citizens (to anyone, actually).
Though your question seems more focused on the former issue, I think you are really more exercised by the latter. You would be very strongly opposed to Australia hanging a "mule" and to Australia punishing a man for having homosexual relations. And you would not be upset, I guess, if an Australian abroad received a punishment you consider just for some culturally specific crime that does not exist in Australia (e.g., having sex with a woman on the basis of a false promise to marry her while knowing that such sex will make her a total and permanent outcast in her community).
As it happens, I am also in Australia and saw a poll last night showing that 47% of Australians want the hanging to go ahead, while 46% are opposed to it. I suppose those 47% think it is alright for someone to be hanged for smuggling 400 grams of heroin and, given that they find this alright, they don't mind it being done by foreigners (assuming the man had a fair trial and so on).
In sum, then, I think we should think about criminal law at home and abroad together, against the background of one single conception of justice. This conception must recognize that the criminal law must be adapted to cultural conditions which may vary from country to country. (In Australia, justice would not be served by jailing men for using a false promise of marrige to entice a women to have sex; but in some very religious countries justice might well be served by such a law.) This conception must further recognize that in some countries harsher punishments for some offense may be appropriate because this type of offense is there more frequent or more harmful or harder to suppress (think of the offense of lighting a fire without a permit). And this conception must also recognize that there is a considerable element of judgment involved in settling upon appropriate punishments: There can be reasonable disagreement over whether a drug smuggling offence of the sort you cite should, in a context like Singapore's, fetch six months in jail or two years. But, contrary to what 47% of your compatriots seem to believe, hanging this young man is a clearcut injustice.