When should I start color correction in Final Cut Pro X?

You’re right to be a little confused—color correction can happen at different stages depending on your workflow. Typically, you'll want to do color correction after you’ve got your picture lock, meaning when the edit is final and the footage is cut together. This way, you’re not redoing work as you make further changes to the timeline. As for doing some color work during the import phase, you can apply a basic color correction to your raw footage at the start, especially if the footage needs some quick adjustments (like exposure or white balance), but the heavy lifting is usually saved for after picture lock when you can focus on each scene and shot individually. So in short: basic fixes early on if needed, but detailed color correction happens after picture lock.

Very last thing you do, while the sound track is being tweaked, traditionally. Since you need to tweak color grading and effects to match clips before and after in the Timeline, you can't really know what other do until you have a final edit of the film.