One of the Great Truths of photography is that for every camera/lens/tripod combination, there is a range of shutter speeds that you need to avoid.

• At faster shutter speeds, the exposure is completed before the system's physical resonance has a chance to blur things

• At slower shutter speeds the system has damped out before the exposure is complete, and the majority of the exposure occurs when the system is essentially motionless.

• It's the speeds in the middle, where the system is in motion for the majority of the exposure, that you need to find and avoid.

That is true of any lens/camera/tripod, but the problem is usually difficult to notice except on a very high-resolution system.

Mirror lock-up can only help a little, since the action of the shutter can be enough to initiate the resonance. Since you are experiencing this problem on only one or two exposures out of a three-shot sequence, I'd be willing to bet money that the shutter speed is what you're changing between exposures and that the problem is occurring consistently in a range of shutter speeds.

In this situation (with the one-shot 360° lens attachment), the problem is exacerbated by the inherent springiness of the mirror stalk. (There are more stable designs, but then you're generally shooting through a cylinder of polycarbonate that's a real sonofabee to keep meticulously clean and unscratched.) Just find out which shutter speeds are causing the problem, and adjust your exposure settings to avoid them. You may want to find the best (least blurry) speed and sharpest aperture, then base your bracket on a varying ISO instead.