7 weeks and my butt is finally jiggling. Does that mean all the fat that’s transferred finally settled in and is here to stay?

The softening of your butt more likely represents the swelling resolving. It takes 3 months to see the final result and confidently say that what you have at that point is what you'll keep. As for exercise, surgeons often have different opinions so it's probably best if you discuss this with your own surgeon. Hope that helps! 

The literature states that fat can be absorbed for up to 6 months post op. In my practice results are pretty stable to the naked eye at 6 weeks as long as you do not lose any weight after that point. I allow my patients to return to exercise at 6 weeks post op. If you didn't do cardio pre-op (start a new more intense workout routine), you risk losing weight.