Congratulation on your wife's JLC watch.
And yes, the "loud" click you heard was the main spring slipping inside the barrel that is designed to release the tension from overwinding. All automatic watch has this feature.
I don't know whether CAL968 is uni or bi-winding. But as a quick test, once you hear those loud clicks, try rotating the watch manually in one direction. If you hear click, then reverse the direction. If you hear click in both directions then it is bi. If not, then it is the super effecent uni-winding autotractor.