Take a look at around 0:15 of the video - it’s clear that the pumping motion of the camera which is synced to the beat is a result of the speed ramping. When it’s slowed down, you can still see the camera shakes, but they’re not as apparent because they’re slow. At the moment where it’s sped up, the camera motion becomes much more apparent because the speed ramping allows more camera movement (shake) in a certain period of time.

Of course, there is no right or wrong order. You can do this by adjusting your shake keyframes to match the beat but if you’re looking to recreate that effect this is my best guess

I believe this is what’s happening in your reference clip. The reason the camera shake looks like it’s synchronized to the music is because the speed ramps up on every beat, causing the camera shake to be more pronounced each beat

If you added the shake after the speed ramping the “intensity” (really frequency) of the motion would remain constant and it wouldn’t look like the reference video

Edit: Your base camera shake would have a constant frequency/motion. The speed ramping would give it the pumping in time to the music

This is a camera shake effect that has been added before the speed ramping. Most video editors can do this effect:

• in Premeire you can keyframe the position, scale, and rotation over time or get premade “camera shake presets” (you can google for them). After this you would nest the clip and do your speed ramping
• in After Effects you can use key framing or expressions on the position/rotation/scale properties or use third party effects like sapphire shake. After this you would precompose the clip and do your speed ramping.