You are correct that it slows down rate of Stability dropping and it is a positive thing. The other option should say "+100% DELAY between two crisis Independent People spawn on all Cities", which means more or less that rebel armies should spawn less often when City Stability hits rock bottom.

It is 'per turn', because Stability isn't lost in an instant, if City, for example, gets hit with "-50 Stability" penalty, it means that its target Stability is now 50 lower and it will travel there across couple of turns. That Civic choice slows it down, so you have even more time to react when City Stability drops low for whatever reason.

EDIT: becaue I just noticed the last question in the OP, 'neither' is a viable option for a Civic as well, if for whatever reason you dislike it or it wouldn't benefit you (Irreligion, for example, is a Civic that I barely even choose, because both choices lock you out of benefit of Tenets and offer next to nothing in exchange). You are not forced to choose in every Civic, although most of them provide some kind of benefit, so more often than not it's worth it if you have some spare influence lying around.