It looks like your arms bone chain and weight paint is waaaaay off.
Almost as if you are using blender’s BB bones on the arms.
Since the mannequin animation apparently works (it’s bad, you should make it way more steady, but it works) - the issue cannot be your animation.
doubleck that you setup your bone as Advanced for both of the rigs to re-target.
test by retargeting other existing mannequin animations (jump start / jump land), anything that moves the arm will either present similar issues, or work.
If any of the mannequin default anims just work, then you may have imported the animation we see on the mannequin with it’s own skeleton instead of using the mannequins skeleton.
Hard to say by just looking at the video.
Like Frankie suggested, you would be better off applying the animations to the skeleton you are actually using directly in a 3D program.
maybe you would even be better off “filming?” Directly on the skeleton you need to animate.