The design editor should have a built-in slider (not the osu!-gameplay kind of slider, mind you
) that allows you to adjust the video's offset, in the event of the two not syncing up like that. Go to the design tab and play around with that.
If you find that the Design Editor's offset adjustment is a bit too difficult to fine-tune, you can directly edit the video offset through opening the .osu file on your favorite text editor, then reloading the file (Ctrl+L or Shift+Ctrl+L). From there, you can experiment to see which is the most ideal offset for your video.
You can edit the offset by adjusting the number next to your video's filename. An example is shown here:
[Events]
//Background and Video events
0,0,"ponponponbackground.jpg"
Video,-9600,"ponponpon_xvid.avi"
Where the -9600 is the offset.