This is a very good question for which I, at least, do not have an answer, but certainly an interest. The original advice was to send the email. That was seemingly superceded by a disposicion issued by Migraciones saying all visas due to expire between March 17 and April 15 had been automatically extended for 30 days, but with no word on visas due to expire beyond April 15.
Nothing appears on the Migraciones website at the moment that updates the disposicion.
The matter is of concern for anyone here as a tourist, on a precaria, or a temporary resident whose current expiry date falls after April 15.
(Regarding going on to New Zealand, that country plans to not simply flatten the curve, but instead erradicate the virus completely before it has a chance to take hold: there was a NYTimes article about this a few days ago. New Zealand is unlikely to open its borders to anyone, let alone travelers, for 12 months or more. Indeed I doubt most countries will be permitting travel in the way we have previously understood it for the forseeable future. The idea is that, if we can, each of us goes to whereever we call home. If we can't travel home, or if we simply have no fixed abode, then the idea I guess is to hunker down for the long haul wherever we happen to be. For people in that situation in Argentina, it is important to know how Migraciones will handle expiring tourist visas, precarias, and residencias while ever the borders remain shut, a situation that is likely to continue for months. )