Please get your history straight - most land-locked European powers didn't get into the colonial game until very late, certainly not in Asia; - the Austrians never (but they had accumulated the Austro-Hungarian empire more or less by marriage contracts - there was one attempt to supply an emperor to the Mexicans, who was duly executed by Revolutionary Forces in Mexico) - the Germans were late-comers in Africa, so were the Italians.
The intricacies of colonialism and when and how would take up whole history books, suffice to say, that, initially, when England and France were forced to leave their colonies either voluntarily or by hook or crook as in the case of France, the major justification for the initial 'invasion' was that they were bringers of civilisation and Christianity and, to justify their high moral ground, they also bestowed citizenship on the new colonials. I.e. all the brown faces some people find so objectionable now in London, often have been citizens of Great Britain for some generations; similarly in France. Of course they came when their own countries turned to mush through civil unrest and power struggles, because the colonial regimes left a power vacuum and often an adiminstrative one as well - I also imagine investment capital left in a hurry as well.
Add to all this the West's continued need for resources (mostly oil); the accumulation of riches by just a few ruling families in many of those ex-colonial countries and you have a recipe for eventual disaster - and people running for their lives to better countries. I won't even touch on the U.S.A.'s rise to world policeman - I pity them more than I am prepared to criticise.
Somehow there is a mechanism in place which generates lots of smaller conflicts (not small by historical standards), rather than world-wide wars and this is regarded as good by the West, but - again - produces refugees.
I don't know the answers, but from personal experience, I believe Australia has a good chance of making multiculturism work, but should keep the endgame of 'integration' uppermost in mind.
I have said before, we need to take a close look at some of our 'rules'. Debate is a good thing.
