What to do when visa application requires disclosure of the titles of articles I have reviewed?
I believe that this sort of disclosure can be ethical, especially to a neutral third party, and when only discussing papers that have already been accepted and/or published elsewhere. (Papers still in the process somewhere else might be different.). Anonymity of referees isn't a deep ethical good in its own right - it has very clear and specific reasons, and this doesn't seem like a relevant violation. 

Consider the reasons why referees are often given anonymity: 1) to allow referees to give honest feedback without fear of (real or imagined) retaliation, 2) to encourage authors to engage with the referee's arguments, not their personality or status, 3) to avoid the appearance/possibility of quid pro quo reviews, and 4) to ensure that broader perceptions of the article are not influenced by knowledge of its referees.

None of these problems would occur by giving the names of articles to a (I'm going to assume) completely uninterested immigration clerk. If you want to be very conscientious, google your contact to make sure they aren't doing immigration processing to make ends meet while an adjunct professor :)