JPEGs don’t have an alpha channel, which defines trasnparency values. Go back to Photoshop and re-open the jpeg. Save it as a .psd, .tga, .tif, .tga, or .png file. All those formats record alpha channel info . Add an empty layer under the original layer. You may have to cut around the original object with the selection and erase tools. Save both layers in the final version and export. Now, the image will show up in fcp with transparency.
Another quick work-around would be to apply the luma key filter to the jpeg to key out the white, but this may not give as good results as saving to a format with an alpha chanel. There may be areas inside the jpeg that also would key out, using luma.