Tax on pension from Cayman Islands

I cannot answer on the Australian pension, on how the Australian tax authorities will deal with it, as this will depend on Australian internal laws. However iro the Canadian pension, I suggest that you read up the double tax treaty between Portugal and Canada - at least the pensions article,  article 18 in the treaty. This treaty has some unusual clauses.  In principle, pensions are taxable by the country of residence.

Basically foreign pensions will be subject to a 10% tax in Portugal under the new nhr rules (or, at the taxpayer's option, per the tax tables - might work out less than 10% in some circumstances)

In respect of pensions from the Caymans - will be treated in the same way as pensions from Australia - the black list is not relevant in respect of pensions, but will be relevant if you receive other income such as dividends or interest from the Caymans - in this case it will be taxed at a penalty tax rate   of 35   % rather than zero.