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I can't help you with Australia or the Dominican Republic, but Canada only taxes residents and "deemed residents", not non-resident citizens.
If you have no "permanent residence" in Canada, spend less than 182 days in the country, and earn no money while in the country, then you are almost certainly not subject to Canadian or provencial income tax.
I'd need to know whether answering just the Canadian tax question would be adequate, before I go into more detail, with cites to CRA documents.
Sorry, I was wrong about "permanent residence"; the term used by CRA is "residential ties", which includes property owned in Canada. However, it seems likely that you are not a Canadian resident, from what you said.