To answer the question with what I think is a workaround because it's not automatic, there's an 'enable_curved_covers' in the settings, for which you can specify at which layer they can turn on (1) or off (0).
In a related matter, the bases of the supports always print in curved covers mode. I find it's an issue because it results in a number of dots or short segments printed without adjacent lines to stop them curling up, before filling in around them. I suspect the algorithm prints the gap infills first, where I reckon they should be last.