I would say that yes, the second line applies when it is played. So when you play provocateur, you increase the unrest by 1 and your opponent gets 1 disgrace. I will change the wording around to make that clearer.
Really, the reason I changed the card in the first place was because its original wording (add 1 unrest each time it's your turn and gain a disgrace each time the unrest track increases) made the card worse than useless for this variant, because there is never a scenario where you want unrest OR disgrace. So something had to be tweaked to make it work, or the card needed to be removed from the deck completely. I went with the former.
In doing so I tried to keep the feel of the card similar to the original version- something that increases the unrest in the city and sticks around, continually causing problems until he's dealt with. So after playing around with a few ideas I went with the current version. I don't expect it to be a game-changing card when it's played, but most personality cards AREN'T game changers. If you look at the other personality cards that grant favor or disgrace, most of them only give a few favor/disgrace. Provocateur can give anywhere from 1-8 disgrace, with the average probably being around 3 or 4 (I think that's just fine, but if people disagree I can increase it to 2 disgrace per Unrest, or to something else entirely).
Plus, I love the risk involved in the card. Increasing the chances that both of you will lose in order to give yourself a bit of an advantage. There were a lot of times in the game my wife and I played where we faced similar dilemmas- (do I solve the problem that is about to erupt and add a couple Unrest, pushing us that much closer to losing, or do I solve this other problem that gives me a better personal advantage?) it makes for some interesting, and fun, decision-making.