My character had his Personality damaged by this blight disease, so I got Almsivi Restoration.
This restored my stat points but I still had the blight and the icon said I still had the personality loss (which I didn't).
Then I went to an Imperial Ctly altar and paid to remove blight and that worked.

Is this normal?

Yes, the main thing to do is cure the disease which also fixes the stats. Restoring the stats separately isn't necessary; that's for damaged stats like from a bonewalker.