Zoom In Using Transform Behaving Oddly

You're only key framing the Scale. You need to also keyframe the Position. Without any keyframing of the Position parameter, yeah, it's where you moved it to be.

Try setting a Position keyframe at the beginning of the clip. If the zooms are too mechanical, you can try the Ken Burns effect. Pan and zoom clips in Final Cut Pro for Mac - Apple Support

Can anyone explain why this is happening?

The cause is clear. You added a keyframe to the expanded item. But because you didn't add a keyframe to the position item.

I think it's better to use the Ken Burns as terryb says.

Since the OP appeared to be new to keyframing, I suggested Ken Burns as something else to try in case the manual keyframing results were not acceptable. I agree manual gives you lots of control but sometimes easing keyframes can result in undesirable behavior, especially for new users.

Well, I'm not a fan of Ken Burns effect. If the OP is trying to zoom in on a specific set of bars in the music to present them, Ken Burns is a horrible way to do it. It's very simple to do manually, takes just as much time, way more precise and accurate.

the only good thing about the Ken Burns is the smoothing/ramping in and out that can be enabled.

I agree with Joe Redifer. When I watched it on YouTube, I felt that the keyframe trajectory seemed unnatural.

If it were me, I would choose Ken Burns because I would like to see the sheet music enlarged smoothly.

Ben, the only good thing about the Ken Burns is the smoothing/ramping in and out that can be enabled. Can't do that with the scaling keyframes... for some reason.