As no-one seems aware of such a tag, you may have to invent one, but first:
Are these buildings signed, on the ground, as evacuation centres?
If not, is there an official, published, list of them that is licensed in a way that is compatible with OSM?
Are different centres used for different sorts of emergency?
Are you prepared to accept that you will need to create your own tools to allow people to find these on the map?
In the UK, any physically suitable council run building is going to be a candidate for this, and some councils may even have a list, but it may well be an internal document. State run schools and council community centres tend to be high on the list, but church halls, and not for profit community centres may also be used.
The actual choice is likely to depend on the emergency and having people turn up at sites that are not being used may actually cause more harm than good…
As such, for the UK, it would probably be better simply to ensure that all suitable locations are on the map, together with details of their operators (although there is also no real way of indicating the distinction between private operators of halls that are likely to help (typically legally charities) and those that might take a more mercenary line).
In practice, in the UK, such places are likely to be the same places as used as polling stations (which are generally not mapped, as such, as they could, in theory change each time, and only apply about one day a year), although for the typical emergencies we have in the UK (flooding, unexploded bombs, and industrial fires) the most local one may be compromised by the emergency. On the other hand, the last thing that the authorities are likely to want is people converging on centres by cars, so there are likely to be people on the ground to direct people to the chosen centre, or to organised transport to it. Also, as I said above, having people turn up at a centre that is not in use may put them at additional risk and strain the authorities.
Where you have semi-predictable emergencies, like tsunamis, and people need to evacuate quickly, I would hope the authorities had already ensured people knew where to go, without having to consult a map at the time.